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COPYRIGHT DEPOSIT 



DESCRIPTIVE ASTRONOMY 



W ELEMENTARY EXPOSITION OF THE FACTS, PRINCIPLES. 
AND THEORIES OF ASTRONOMICAL SCIENCE 



By 

FOREST RAY MOULTON, A.B., Ph.D. 

PROFESSOR OF ASTRONOMY, THE UNIVERSITY OF CHICAGO J RESEARCH 

ASSOCIATE, CARNEGIE INSTITUTION OF WASHINGTON) MEMBER, 

NATIONAL ACADEMY OF SCIENCES; FELLOW, ROYAL 

ASTRONOMICAL SOCIETY; AUTHOR OF "CELESTIAL 

MECHANICS," "PERIODIC ORBITS" 



ILLUSTRATED 



AMERICAN TECHNICAL SOCIETY 
CHICAGO 

1921 



QB- 



6 



COPYRIGHT, 1912, 1917, 1920. BY 
AMERICAN TECHNICAL SOCIETY 



COPYRIGHTED IN GREAT BRITAIN 
ALL RIGHTS RESERVED 



CI.A571902 



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INTRODUCTION 

ASTRONOMY has the glory of being the oldest science. In 
fact, men first realized from the majestic and relatively sim- 
ple motions of the heavenly bodies that the universe is a universe 
of order and, therefore, that science is possible. If the sky had been 
always cloudy, if observations could not have extended beyond the 
exceedingly complex and varying terrestrial phenomena, it is prob- 
able that many centuries would have passed before scientists would 
have arrived at the point of view which was necessary for the devel- 
opment of those ideas which have led to the wonderful discoveries 
of modern times. It is appropriate, therefore, that a book on Astron- 
omy should, among other things, show the connection of celestial 
phenomena with the important intellectual achievements of civilized 
man, a phase of the subject which has not been neglected in this 
work. 

C There are two chief features to science — the making of observa- 
tions, and the fitting of them into an organized whole. In this text 
detailed instructions have been given so that the reader may make 
such of these observations as do not require the use of instruments, 
but it is evident that such observations can not add much to the 
world's knowledge at the present time. However, their performance 
demands the active instead of the passive attitude of the mind; they 



give something of the satisfaction that is experienced by an original 
discoverer; and they make every glance at the familiar stars which 
fill the sky on a cloudless night one of pleasure. Great care has 
been taken also to show how the vast multitude of things, which 
observations have revealed, are linked together into a systematic 
body of doctrine, and entitle Astronomy to be regarded as one of 
the most perfect sciences. 

C Doubtless every person has some more or less definite conception 
of what the universe is and means, and of his place in it. All the 
things he knows and experiences modify this conception. The facts 
revealed in Astronomy — the extent, variety, and lawfulness of the 
physical universe; that man has in his body the elements of which 
the infinitely distant stars are composed; that he is but a part of 
the universal order — effect profoundly his philosophy; and this has 
been borne in mind in setting forth modern ideas of how tenuous 
nebulas evolve into finished worlds 



CONTENTS 



PRELIMINARY CONSIDERATIONS 

Page 

Value of science 1 

Origin of science * . 2 

Great contributions of astronomy to science 3 

Present value of astronomy 4 

Scope of astronomy 6 

THE EARTH AS AN ASTRONOMICAL BODY 

Astronomical problems respecting the earth 7 

Proofs that the earth is round 8 

Oblateness of the earth 10 

Size of the earth ; . 13 

Different kinds of latitude 13 

Density of the earth 14 

Condition of interior of the earth 15 

Composition of the earth's atmosphere 18 

Height of the earth's atmosphere 18 

Kinetic theory of gases 21 

Escape of atmospheres 23 

Effects of atmosphere on climate 25 

Refraction of light by the atmosphere 28 

Relative rotation of the earth 30 

Laws of motion 32 

Rotation of the earth proved by eastward deviation of falling bodies. ... 34 

Rotation of the earth proved by its shape 35 

Rotation of the earth proved by Foucault's pendulum experiment 36 

Analogy with other heavenly bodies 37 

Uniformity of the earth's rotation 38 

Variation of latitude 40 

Apparent motion of the sun with respect to the stars 42 

Revolution of the earth proved by the parallax of the stars 44 

Revolution of the earth proved by aberration of light 4(> 

Revolution of the earth proved by the spectroscope 47 

Shape of the earth's orbit 48 

Obliquity of the ecliptic 49 

Precession of the equinoxes 50 

Causes of the seasons 51 

Relative amounts of sunlight in different latitudes 54 

Lag of the seasons 57 

Effect of the eccentricity of the earth's orbit upon the seasons 58 



CONTENTS 

Page 
THE CONSTELLATIONS 

Problem of locating the constellations 61 

Geographical system 62 

Horizon system 63 

Equator system 64 

Ecliptic system 67 

Comparison of systems 68 

Determination of right ascension of meridian at any time *69 

Application of declination to location of stars " 71 

Origin of constellations 72 

Naming the stars 79 

Star catalogues 80 

Magnitudes of stars 82 

First-magnitude stars 85 

Number of stars 85 

Proper motions of stars 87 

Milky Way or Galaxy : 88 

How to find the pole star 90 

Cassiopeia 92 

Equinoxes 93 

Lyra 93 

Scorpio 95 

Bootes 95 

Leo 96 

Taurus 96 

Orion 97 

Canis major 100 

Gemini 100 



TIME 

Definition of equal intervals of time 100 

Sidereal time 101 

Solar time 102 

Mean solar time 103 

Standard time 105 

Civil and astronomical days 107 

Place of change of date 107 

Sidereal year 108 

Tropical year 108 

Calendar 109 

THE MOON 

Moon's apparent motion among the stars 110 

Moon's phases Ill 

Distribution of sunlight and moonlight 113 

Distance of the moon 113 

Moon's actual motion .' 117 



CONTENTS 

Page 

Size of the moon 118 

Mass of the moon 110 

Atmosphere of the moon 120 

Light and heat received by the earth from the moon 121 

Temperature of the moon 122 

Surface conditions on the moon 123 

Eclipses of the moon 131 

Eclipses of the sun 132 

Relative number of eclipses of sun and moon as observed from any one 
place ,..,.,, 133 



THE SOLAR SYSTEM 

Members of the solar system 137 

Orbits of the planets 138 

Law of gravitation 139 

Distances of the planets 141 

Dimensions and masses of planets 144 

Periods of the planets 147 

Two groups of planets 151 

Planetoids 152 

Zodiacal light and gegenschein 157 

Mercury and Venus 159 

Mars 161 

Jupiter 170 

Saturn 175 

Uranus 179 

Neptune 181 



COMETS AND METEORS 

Orbits of comets 185 

Dimensions and masses of comets 186 

Capture of comets 187 

Celebrated comets 190 

Meteors or shooting stars 192 

Relation of comets and meteors 194 

Influences of meteors on the earth 195 

Meteorites 196 



THE SUN 

Light and heat received from the sun 197 

Source of the sun's heat 200 

Sun spots 204 

Different layers of the sun . 206 

Spectrum analysis 210 



CONTENTS 

Page 
THE SIDEREAL SYSTEM 

Distribution of stars 216 

Groups of stars , 219 

Double stars 224 

Spectroscopic binary stars 227 

Variable stars 229 

Temporary stars 231 

Nebulas . 2£3 

COSMOGONY OR THE EVOLUTION OF WORLDS 

Evolution 235 

Historical 237 

Test of the Laplacian theory 241 

Planetesimal theory 244 

Conclusion 250 




THE GREAT YERKES 40-INCH TELESCOPE 
The dome is revolved by machinery and the entire floor is raised or lowered to suit the inclination of 

the telesoope tube 




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ASTRONOMY 

PART I 



PRELIMINARY CONSIDERATIONS 

The Value of Science. In an age when the world is so largely 
run by the results of scientific effort it is almost superfluous to 
speak of the value of science. If the things which science has con- 
tributed to our everyday use and which make life at the present 
time pleasant for us were removed, we should speedily understand 
the immense debt we owe to it. One has to think only of the means 
of transportation, communication, and illumination to see how very 
important it is for us. These things are so well known that they 
do not need emphasis. 

There is an indirect result in the work of scientists which is not 
so generally understood, and to which we seldom give any considera- 
tion. Science has revolutionized our mode of living, that is, it has 
given us a better food supply than any people ever had; because of 
it, we are better sheltered and clothed than any people ever have 
been; our whole mode of living is more sanitary than that of any 
other people has been; and these facts will eventually result in 
marked physical changes in mankind as the generations go by. Thus, 
while we are apt to consider that science pertains largely to the 
inanimate part of the universe, we see that it is not only of the highest 
value indirectly to the organic portion, but to man as well. If we 
are considering things in the long run, this latter may be the one 
respect in which it is most valuable. 

It is a common opinion that science is distinguished from the 
fine arts and, in fact, is opposed to them. Science and the fine arts 
are very often supposed to be the antithesis of each other. But one 
of the results of science has been that it has made us immensely 
more efficient than we were before, and through its teachings we are 
enabled to provide the necessities and even the luxuries of life in 
much less time than was possible before its modern development. 



2 ASTRONOMY 

The leisure which has been secured thereby will enable us to turn 
our attention to the arts and undoubtedly in the future to achieve 
greater things in this direction than would otherwise have been 
possible. 

It is a mistake to regard science in itself as the opposite of art. 
There are in all branches of science harmonies and beauties which 
appeal strongly to those who fully understand them. The great* 
scientists have often expressed themselves as deeply moved by the 
esthetic side of their subject. 

Science also plays an important role in the mental discipline. 
If it is a good thing to think coherently and systematically and to 
check the results of thinking, then science is of the highest value in 
the cultivation of the intellect. 

Origin of Science. It is doubtful if any important idea ever 
sprang suddenly into the mind of a single man. The great move- 
ments in the world have had long epochs of preparation, and there 
are evidences that many men were groping for the same idea without 
exactly seizing it. 

The actual dawn of science was in prehistoric times, in the 
civilizations that flourished in the valleys of the Nile and the 
Euphrates. In the very earliest records that have come down to us 
it has been found that those peoples knew much of astronomical 
phenomena and had coherent ideas of the apparent motions of the 
sun, moon, planets, and stars. It is perfectly clear from their 
writings that it was first in observing celestial phenomena that 
they obtained the idea that the universe was not a chaos. Day and 
night were seen to succeed each other regularly, the moon passed 
through its phases systematically, the seasons followed one another 
in regular sequence; and in fact all the more conspicuous celestial 
phenomena were seen to recur in an orderly fashion. The dawn of 
science may be said to have begun when men first clearly perceived 
that there was order in the universe and that by observations they 
could discover what it was. It is to the glory of astronomy that its 
phenomena were of such a character that men first perceived in this 
realm that we live in an orderly universe. 

The ancient Greeks, at a period four or five hundred years pre- 
ceding the Christian Era, definitely undertook to find from systematic 
observations how celestial phenomena follow one another. Before 



ASTRONOMY 3 

their time, observations were, indeed, made extending over long 
intervals, but without a conscious effort to attain the laws according 
to which the universe moves. The Greeks determined very accu- 
rately the number of days in a year, the number of days in a month, 
the path of the moon among the stars; they explained the cause of 
eclipses and learned how to predict them with a considerable degree 
of accuracy; they undertook to determine the distances of the 
heavenly bodies, and to work out a complete system that would 
represent their motions for indefinite time. The idea was current 
among the Greek philosophers that the earth was round, that it 
turned on its axis, and among some that it revolved around the sun. 
Their science, in the modern acceptance of the term, was largely 
confined to the study of celestial phenomena. 

Great Contributions of Astronomy to Science. As has been 
stated, science started in astronomy. The phenomena of every other 
science are so complex and depend upon so many varying factors 
that it would be very difficult for a primitive people to get the idea, 
first, that there were any laws operating in it, and second, that they 
could discover those laws. One has to think only of the complexities 
in the changes of the weather or in the developments of plant or 
animal life, to see how hopeless a problem a primitive people would 
face. It is probably not extravagant to state that if men had not 
been able to observe celestial phenomena — for example, if the sky 
had always been cloudy — the dawn of science would have been 
greatly delayed. It is entirely possible that we should yet be in the 
most primitive stages of the development of the race. 

But we may turn our attention to more specific and direct con- 
tributions of astronomy. Every one will admit that mathematics 
has been of the highest service in all domains of physical science. 
It is not so generally known that the science of mathematics was 
largely called into being for uses in explaining astronomical phenom- 
ena. Spherical trigonometry was invented in very ancient times for 
use in solving the problems arising from the celestial sphere. And 
this is only one of the many examples in which some of the most 
important mathematical processes have been directly developed 
as a consequence of the stimulus of a problem set to men in 
astronomy. While it would undoubtedly be too much to ' claim 
that all branches of mathematics have had their original stimulus in 



4 ASTRONOMY 

astronomical problems, it is certain that without these problems the 
development of mathematics would have been far different. 

The laws of motion are at the very foundation of modern 
mechanics, and were discovered by astronomers contemplating 
astronomical phenomena. The conditions on the earth are so 
complex that it would be very difficult to comprehend the funda- 
mental laws which govern the movement of bodies. On the contrary, 
the planets move in a vacuum without any friction, and the con- 
ditions are so nearly ideal that discovery of these fundamental 
laws is relatively simple. It is not too much to say that our knowl- 
edge of the laws of motion is a contribution from astronomy. 

One of the most important influences in modern scientific thought 
is the doctrine of evolution. Its applications are not only in geology 
and zoology, but they are also in the interpretation of history, 
sociology, and even religion. It was in contemplating the relatively 
simple celestial phenomena that the idea of the orderly development 
from one state to another was first clearly perceived, and the doctrine 
of evolution was current in astronomical literature more than half a 
century before it appeared in the writings of Darwin and his con- 
temporaries. 

The modern world owes much to the explorations that followed 
the voyage of Columbus across the sea. It took courage of the highest 
type to sail for many weeks over an unknown sea in the frail boats 
of that time. It is perfectly clear that Columbus had good reasons 
for hoping that he could reach the East Indies by sailing westward 
from Europe, for otherwise he would not have maintained control of 
his mutinous sailors for so long a time. His reasons were of an 
astronomical nature. He had seen the sun rise from the ocean in 
the east and travel across the sky and set in the west. He had 
observed that the moon and stars did the same thing. He concluded 
from the fact that they went down in the west after having pursued 
regular courses, and rose again in the east in the same courses, that 
the earth was not of infinite extent but that it was round and 
could be sailed around. Relying upon the teachings of his observa- 
tions of the motions of the heavenly bodies, he made the perilous 
trip across the Atlantic, and that voyage has been of immense 
importance to the human race. 

Present Value of Astronomy. It is easy to see, as has been 



ASTRONOMY 5 

explained above, that astronomy has made some great contributions 
to the development of science and civilization; but it is commonly 
believed that at the present time it is of little practical value to 
mankind. This is known as a material age and we are apt to con- 
sider things valuable only if they are valuable in a material way. 
But if astronomy is considered from this point of view, we still find 
that it is very important to us. For example, navigation of the seas 
is absolutely dependent upon astronomical observations. For more 
than two centuries France and England gave prizes for accurate 
astronomical tables that their sailors could use in their journeys 
over the oceans. And at the present time the positions of vessels 
are determined in all long voyages by astronomical observations. If 
one were to make a voyage to the polar regions he would determine 
his position, and in particular whether he had arrived at the earth's 
pole or not, by astronomical observations. Consequently, we may 
say that all the varied and important interests which center in 
navigation are dependent, even at the present time, upon astronomy. 

One might imagine that, even though astronomy is important to 
sailors, it has little value upon the land. Here, again, the first 
impression is quite erroneous. Every one recognizes how important 
it is that our trains be run according to accurate time schedules. 
It is not so generally known, however, that the time used is based 
upon astronomical observations made daily. In the National Observa- 
tory at Washington observations are made and time is determined 
and distributed every day over the whole country. More than 30,000 
clocks are automatically set every twenty-four hours by the electric 
signals which are sent out from Washington. 

One might ask whether some other method of accurately meas- 
uring time might not be devised. The general impression is that a 
clock might be made to run so accurately that it would serve all 
purposes. The fact is, no clock was ever made which permanently 
ran accurately. No two can be made to run exactly alike. In order 
to obtain a satisfactory measure of time, the ideal conditions under 
which the heavenly bodies move must be realized. Consequently, a 
second practical and universal use of astronomy is in furnishing time 
for mankind. 

There are indirect ways in which astronomy is at the present time 
of great value. For example, if it be conceded that geology is an 



6 * ASTRONOMY 

important science, then astronomy must be considered valuable 
because it furnishes the foundation for the geologist in telling him 
of the early state of the earth. If it is important for man to know 
the laws of change of the weather, then astronomy is again important 
because the reasons for the changing of the weather are almost 
entirely astronomical. In this example we have not yet learned 
fully the laws because they depend partly upon complex conditions 
that are present here upon the earth. The simple succession of 
changes that would follow from astronomical causes alone on a 
uniform earth are modified by great oceans, continental elevations, 
and chains of mountains. Notwithstanding the complexity of these 
factors, there is hope of eventually reducing this domain of science 
to perfect order. 

While this is called a material age it is probably not more so 
than most which have preceded it. And if it is not purely a material 
age, in estimating the value of any science it is proper to consider 
its importance- aside from its practical applications to the material 
world. When considered from this point of view astronomy is 
probably second to no other science. It furnishes man an idea 
of his place in the universe and has a profound influence upon 
him in broadening his horizon. It is analogous to the benefits a 
man derives by traveling on the earth. If he visits various countries 
he learns many things which he does not directly apply at his home, 
but which, nevertheless, make him a broader man. And so, while 
what one may learn about worlds beyond our own can not, on the 
whole, be applied here, the broadening influence of the wider knowl- 
edge is very beneficial. In this w T ay astronomy has had and is having 
profound influence on philosophy and literature and even religion. 

Scope of Astronomy. In astronomy the earth is considered first 
as a member of the solar system. It is thought of as a member of 
a family of planets revolving around the sun. Its characteristics as 
one of the heavenly bodies are investigated. They are, in particular, 
its shape, its size, its motions, its density, and its interior condition. 
Then the details of its relations to other members of the system are 
developed and the corresponding facts for the other planets and the 
sun are worked out. 

There are many secondary members of the planetary system, 
among which may be mentioned the satellites which revolve around 



ASTRONOMY 7 

the planets, the comets which revolve around the sun, and a great 
number of small planets which circulate mostly in the space between 
Mars and Jupiter. The motions of these bodies and their proper- 
ties, and their relations to the rest of the system are worked out. The 
thousands and even millions of stars that fill the sky are found to be 
suns, and the position and relation of the solar system with respect 
to the almost countless other systems, particularly the distribution 
of stars in space, their motions and dimensions, are discovered so 
far as it is possible. There are also found to be immense cloud- 
like masses of unorganized world-stuff which we call nebulae, w T hose 
number, positions, and relations to the stars are discovered. 

In addition to finding out what the universe is at the present 
time, one of the most important and interesting objects of astronomy 
is to find out how it originated, through what series of steps it has 
gone in its evolution, and what changes will take place in it in the 
future. In particular, the astronomer tries to find out what has 
been the origin of the earth, how long it has been in existence, espe- 
cially in a state adapted to the abode of life, and what reasonably 
may be expected for the future. These great problems of cosmog- 
ony have been of interest to mankind from the dawn of civilization, 
and with increasing knowledge they do not lose their charm. 

THE EARTH AS AN ASTRONOMICAL BODY 

Astronomical Problems Respecting the Earth. The earth is 
one of the objects belonging to the field of astronomical investiga- 
tions. It is in considering it that astronomy has its closest contact 
with some of the other sciences, particularly with geology and meteor- 
ology. Those problems which can be solved for the other planets 
also, or which are essential in the investigations of other astronomical 
questions, are properly considered as belonging to the field of astron- 
omy. 

The astronomical problems pertaining to the earth are divided 
into two general classes. First, there are those questions which 
can be answered, at least to a great extent, without considering the 
earth as a member of the solar system. Second, there are those 
problems which pertain to it as a member of the solar family. Those 
of the first class are particularly its shape, size, density, rigidity, and 



8 ASTRONOMY 

its atmosphere; while those of the second class are particularly its 
motions, the heat and light received from the sun, and its evolution. 
We shall take up first the questions of the first class. 

Proofs That the Earth Is Round. It is a matter of common 
knowledge that the earth is approximately round, but few can give 
the reasons for believing it. One of the characteristics of science 
is that it gives the reasons for its conclusions, and consequently we 
shall consider the methods by means of which we have proved the 
sphericity of the earth. 

The most commonly stated reasons are that the earth has been 
circumnavigated and that the surface is apparently convex. While 
this proves that the earth is not an infinite plane, as the ancients 
believed it was, it does not prove it is actually round; for these con- 
ditions could be satisfied if its surface were any closed, convex figure, 
even departing very widely from a spherical form. There are bet- 
ter reasons for believing that the earth is actually very nearly spher- 
ical. In taking them up we shall first suppose that it is actually 
a perfect sphere, and then later consider its slight deviations from the 
globular form. 

The simplest and most certain proof of the globular form of 
the earth is that the plane of the horizon, or the direction of the 
plumb line, changes by an angle which is directly proportional to 
the distance traveled along the surface of the earth, whatever be 
the starting point, direction of travel, and distance traveled. This 
statement needs some amplification. Let us suppose first that the 
earth is a sphere and show that the statement is true. 

In Fig. 1, let the circle represent the earth whose center is at 
C, and let us suppose that the stars are very far away from it com- 
pared to its size. Suppose the line CP points to the pole of the sky. 
Suppose an observer is at X . He will observe the pole in the direc- 
tion O1P1, which is parallel to CP if the stars are supposed to be 
infinitely far away compared to the size of the earth. The plane of 
his horizon is H x . If he stands at X and looks north he will look 
in the direction H^ The angle between the plane of the horizon to 
the north and the line from the observer to the pole is a v 

Now let us suppose he travels northward to point 2 . Then 
the direction to the pole becomes 2 P 2J which is again parallel to 
CP. His horizon in this case is H 2 . The distance of the pole above 



ASTRONOMY 



the horizon is now the angle a 2 . He has gone along the surface the 
distance Ofl-z, which subtends the angle a at the center of the earth. 
We wish to prove that the direction of his horizon is changed by the 
same angle. This follows at once because the lines Hi and H 2 in 
the figure are, respectively, perpendicular to C0 X and C0 2 , and there- 
fore by plane geometry the angle between H l and H 2 is equal to the 
angle between CO x and C0 2 ; that is, the change of direction of the 
horizon is equal to the angular 
distance the observer has trav- 
eled along the surface of the 
earth. If the earth is spherical, 
the actual distance along the 
surface in miles is proportional 
to the angle subtended at the 
center. Consequently, the orig- 
inal proposition is verified. 

There is no other figure 
than the sphere for which the 
plane of the horizon will change 
proportionately to the distance 
traveled. Consequently, if it 
is found that as one travels Fl 5 
over the surface of the earth 
the change in direction of the plane of the horizon is in direct 
proportion to the distance he travels, it proves that the earth 
is an exact sphere. In Fig. 1, the question was considered only for 
a motion north and south. The reason for this was that the north 
star remains fixed in the sky while the other stars appear to move 
around the earth in diurnal circles just as the sun and moon do. 
Therefore, it is simpler actually to make the observations for north- 
ward and southward motion, and it is also easier to understand the 
matter. However, in order to show that the earth's curvature is 
the same in every direction, it is necessary to prove the proposition 
in the general form given at the beginning. 

That this is the simplest method of proving the shape of the 
earth is supported by the fact that it was the one first discovered 
and used. The Greek astronomer, Eratosthenes, more than two 
hundred years B.C., noticed that the north star appeared to be higher 




A Diagram Showing That the Elevation 
of the Pole of the Sky Varies Proportionally to 
the Distance Traveled Along a Meridian 



10 



ASTRONOMY 



when he was in Greece than it did during his journeys farther south 
in Upper Egypt. He correctly interpreted this as meaning that 
the earth was convex, and he assumed it was spherical. In fact, he 
went so far as to try to find the size of the earth by measuring the 
distance he had to travel over its surface to cause the pole star to 
change its elevation above the horizon by one degree. While* at 
that very early date correct ideas of the shape of the earth were 
entertained by a few and attempts were actually made to find its 
size, nevertheless the belief in the roundness of the earth perished 
because of the lack of the scientific spirit and the mysticism of antiq- 
uity. There was no general acceptance of the fact that the earth is 
round until after Columbus had crossed the Atlantic and his imme- 
diate followers had circumnavi- 
gated the globe. 

Oblateness of the Earth. In 
the preceding section a method 
of proving the sphericity of the 
earth was given, providing the 
earth were actually spherical. If 
it is not perfectly round, obvi- 
ously the method ought to reveal 
this fact. As a matter of fact it 
has been found that the earth is 
slightly flattened at the poles and 
bulged at the equator. We shall 
now see how the observations 
have shown this to be true. 
Let us first suppose that the earth is flattened, as has been stated, 
and see what the observation should show. In Fig. 2, let the curve 
E represent a section of the earth through its axis and perpendicular 
to its equator. Let the circle C 1 be a circle which has the same curva- 
ture as the earth at its equator, and let the circle C 2 be that one 
which has the same curvature as the earth at its pole. It is clear 
from the figure that d is smaller than C 2 . Consequently, if one were 
to go a degree north or south on the earth at its equator he would be 
going a distance equal to one degree on the circle C lt and if he were 
to go a degree north or south on the earth near the pole he would be 
going a distance equal to one degree on the circle C 2 ; that is, a dis- 




Fig. 2. The Curve E Is a Section of the Flat- 
tened Earth; C\ Is a Circle Having the Curva- 
ture of the Earth at Its Equator, and C 2 One 
Having the Curvature of the Earth at Its Pole 



ASTRONOMY 11 

tance corresponding to one degree as measured by the difference in 
direction of the pole is less at the equator of the earth than it is at 
the pole of the earth if the earth is flattened. On the other hand, 
if the earth were elongated in the direction of its axis the opposite 
result would be true. 

The actual shape of the earth was under discussion for a long 
time, the English, following Newton, taking the position that it is 
flattened at the poles and bulged at the equator; and the French, 
who were generally opposed to the English in everything, taking 
the position that it is flattened at the equator and bulged at the 
poles. About 1745 the French measured an arc in Lapland near the 
Arctic Circle, and another in Peru near the equator. They found 
definitely that the arc one degree in length was longer in Lapland 
than it was in Peru. This proved beyond any question that the 
earth is flattened at the poles and bulged 
at the equator, and besides it gave the 
amount of the flattening. 

Newton's prediction that the earth 

would be found by observations to be 

oblate is one worthy of notice. Relying 

on the fact that the earth rotates he was 

able to prove it. In Fig. 3, let PP' be 

the axis around which the earth rotates, 

^^ 

and Q a point On its equator. Newton Fig. 3. Newton's Canal Proof 
, , J , „ ~ , That the Earth Is Oblate 

imagined a canal constructed from P to 

C, the center of the earth, and then from C to Q. The rotation of 
the earth has no effect upon the weight of the water in the canal 
PC. But the rotation decreases the weight of every unit volume 
of water in the canal CQ, the amount of the decrease depending on 
its distance from the axis. Now, if the two canals are to be in 
equilibrium the pressure of PC at C must be exactly equal to the 
pressure of QC at C. Since each unit volume in QC exerts a less 
pressure than the corresponding one in PC, it follows that the canal 
QC must be longer than the canal PC. It is not a simple matter to 
find how much longer it must be, yet Newton solved the problem 
and his results have been verified. 

There is a third method of proving the existence of the equa- 
torial bulge of the earth. The moon is kept in its orbit around the 




12 



ASTRONOMY 




Fig. 4. The Moon's Attraction for 

the Equatorial Bulge of the Earth 

ffects Rotation and Proves 

That There Is a Bulge 



earth by the earth's attraction for it. Now, the attraction of the 
earth on the moon is not quite the same if it is oblate as it would be 
if it were strictly spherical. This variation in attraction will cause 
a corresponding small change in the motion of the moon. When the 
amount of the equatorial bulge is known, the irregularities produced 
by it on the motion of the moon can be computed. As a matter of 

fact they have been computed and it has 
been found that the motion of the moon 
has exactly those irregularities which it 
should have if the earth were oblate, thus 
verifying the fact of its oblateness. 

Conversely, the attraction of the moon 
for the earth is different from what it 
would be if the earth were spherical. 

In Fig. 4, let E represent the largest 
sphere which can be cut out of the flat- 
tened earth. The attraction of the moon 
has no effect on the rotation of the sphere, but its attraction on the 
equatorial bulge, A and B, does have an effect upon the rotation of 
the earth. This effect is actually observed and proves that the earth 
is bulged at the equator. Not only do all these proofs agree in 
showing that it is oblate, but they also agree in the determination 
of the amount of the oblateness. 

It is not sufficient to say that the earth is flattened at the poles 
and bulged at the equator, but it is necessary to describe more exactly 

its form. In order to do this we must 
define the curve called an ellipse, which 
is represented in Fig. 5. 

The ellipse is an oblong, closed curve, 
such that the sum of the distances from 
two fixed points within, F and F' ', to any 
point P on its circumference is always the 
same. It follows from this definition that 
a convenient way to draw it is to set two 
pins at F and F' in the drawing-board and to tie the ends of a string, 
whose length is somewhat greater than the distance FF', to them. 
Then if a pencil is put in the string at P and held tight, the circum- 
ference of the ellipse can be easily traced out. 




Fig. 5. An Ellipse of Which 
the Foci Are F and F' 



ASTRONOMY 



13 



If the ellipse be rotated around the diameter BB' it generates 
a solid which is called an oblate spheroid. Its shape is roughly like 
that of an orange. If it were rotated around the longest axis, A A', 
it would generate what is called a prolate spheroid, whose shape is 
similar to that of a long watermelon. Now, the shape of the earth 
is very nearly that of an oblate spheroid, though the amount of 
flattening is so small that if it were drawn to scale it would appear to 
the eye as sensibly spherical. There are some slight deviations from 
the oblate spheroidal figure due principally to the continental eleva- 
tions and the irregularities in the distribution of matter. 

Size of the Earth. The measurements of the arcs on the 
surface of the earth not only prove its shape but furnish us directly 
its size. It has been found in this way that its mean diameter is 
about 7,910 miles. The equatorial dia- 
meter is about 27 miles greater than the 
polar, owing to the flattening of the earth. 
According to the most accurate observa- 
tions and computations so far made, the 
equatorial diameter is 7,926.7 miles, and 
the polar diameter 7,900 miles. Accord- 
ing to this the equatorial circumference 
of the earth is 24,902 miles. 

From the figures given above it is 
found that one degree in latitude at 

the earth's equator equals 68.7 miles, and at the pole, 69.4 miles; 
that is, a degree at the pole is about one per cent longer than one 
at the equator. In longitude, one degree at the equator equals 
69.7 miles. In latitude forty degrees, one degree in longitude 
equals 53.4 miles. In latitude sixty degrees, one degree in longitude 
equals 34.9 miles and, of course, at the pole there is no such thing as 
longitude. 

Different Kinds of Latitude. Since the earth is not a perfect 
sphere, a perpendicular to its surface (i.e., water level surface), at 
any point except on the equator or at the poles does not pass through 
its center. This gives rise to different kinds of latitude. 

In Fig. 6, let P represent the pole of the earth, E a point on its 
equator, and C its center. Suppose an observer is at and that OA 
is perpendicular to the surface at 0. The geocentric latitude is the 




Fig. G 



The Geocentric Latitude 
Is ai and the Astronomical 
Latitude Is a* 



14 ASTRONOMY 

angle ECO^a^ The astronomical latitude, i.e., the latitude which 
would be found by astronomical observations, is the angle a 2 . It 
is seen from the figure that the astronomical latitude is a little greater 
than the geocentric latitude. 

Density of the Earth. In measuring the densities of solids and 
liquids it is customary to use water at its greatest density .as 
the standard. It is necessary to state that the density of water 
at a given temperature is used as the standard because it varies 
with the temperature. If we start with a very high temperature 
the density increases as the temperature falls until it reaches about 
39° F., after which the density begins to decrease. If this were not 
so, ice would be denser than w T ater and would sink instead of float. 
When it is said that the density of rock is three, it is meant that 
a given volume of rock weighs three times as much as the same 
volume of water at its greatest density. 

It is a simple matter to determine by direct examination the 
densities of those materials on the earth which are so near its surface 
they can be actually reached. But when it is understood that the 
deepest borings in the earth reach to a depth of about two miles 
only, which is only toVo of the distance to the earth's center, it is 
clear how small a part of the earth's mass comes directly under our 
observation. It is, therefore, necessary to discover some indirect 
method of finding the density of those parts which lie so deep we 
can not reach them. 

The volume of the earth being known, its density can be found 
provided we can discover some way of finding its mass. The masses 
of all astronomical bodies are found by their attractions for known 
bodies. The attraction of the earth for masses at its surface is what 
gives them weight. It is possible, though it is a very delicate experi- 
ment, to compare the attraction of the earth for a small ball with that 
of a large ball for the same small one. The delicacy of the experi- 
ment comes from the fact that the force of gravity is so feeble that 
it is with great difficulty that the attraction of the large ball for the 
small one can be measured. Let us suppose, however, that it has 
been measured, as is actually the case in many experiments which 
have been carried out, and let us see how the mass of the earth can 
be determined. The attraction of one body for another depends 
upon two chief factors, viz, the mass of the attracting body and 



ASTRONOMY 15 

its distance from the attracted body. Now, in the experiment of 
comparing the attraction of the earth with that of a large ball for 
a small ball, the distances of the earth and the large ball from the 
small one are known. The relative attractions are measured. The 
density of the large ball and, therefore, its mass are known. The 
only unknown in the proportion is the mass of the earth; or, since 
its volume is known, the only unknown is its density. By means 
of these measurements and the discussion of them, it has been found 
that the average density of the earth taken through and through 
is about 5.5. The average density of the surface rock with which 
we are familiar is from 2.75 to 3. This means that the interior is, 
on the whole, considerably denser than the surface rock. Two 
explanations of this are possible: First, the material of which the 
interior is composed may be largely of dense substances; second, 
it may be that the great pressures which prevail in the interior are 
sufficient to squeeze ordinary matter to such an extent that its 
density is increased enough to account for the greater density of the 
interior. 

The pressure on the interior of the earth is enormous. The 
weight of a cubic foot of water is, in round numbers, 60 pounds, and 
of the surface rock approximately 180 pounds. If we stretch this 
cube out into a parallelopiped, whose base is one inch square, its 
height will be 1,728 inches (since there are 1,728 cubic inches in a 
cubic foot), or 144 feet. The pressure of this column on its base 
will be its weight of 180 pounds. The pressure on such a column of 
one-inch cross-section at the depth of one mile will be tWX180 = 
6,600 pounds. The pressure at the depth of 100 miles, therefore, will 
equal 330 tons per square inch, which is a very moderate depth 
when the earth as a whole is considered. It is ^easily conceivable 
that these enormous pressures are sufficient to give ordinary matter 
a density of 5.5, and consequently there is no reason to believe from 
these considerations that the material of which the interior of the 
earth is made is, on the whole, radically different from that which is 
near its surface. 

Condition of Interior of the Earth. It has been very generally 
believed until recent times that the interior of the earth is in a fluid 
state, owing to the high temperatures prevailing there. It has been 
found that the temperature rises about 1° F. for every 50 to 100 feet 



16 ASTRONOMY 

that one goes down in the earth. The rate of increase of temperature 
varies greatly at different places. But taking the slowest rate 
observed, it is seen that if it continues to great depths the temperature 
of the interior must be very high. Suppose, for example, that the 
increase of temperature is only one degree for 100 feet. Then the 
increase of temperature at the depth of a mile would be 50 degrees.* 
At the very moderate depth of 100 miles we should find a temperature 
of 5,000 degrees, which would not only liquefy but vaporize most 
substances. It has been inferred from this that the interior is in a 
molten state, which has been further proved by the expulsion of 
melted rock material from volcanoes, these having been interpreted 
as cracks through the solid crust covering the fluid interior. 

In these conclusions regarding the condition of the interior of 
the earth a very important factor has been neglected. It was 
remarked above that the pressure at moderate depths in the earth is 
very high indeed. Now pressure tends to keep matter in a solid 
state in spite of high temperature. That is, if a temperature of 2,000 
degrees will melt a substance at ordinary atmospheric pressure, a 
temperature of 3,000 degrees might be required to melt it if it were 
subject to a great pressure. While the combination of such extremely 
high pressures and temperatures as prevail in the interior of the 
earth have not been realized in experiments, still there is room for 
doubt as to the conclusion regarding the fluidity of the interior of 
the earth. The effects of pressure in retarding the melting are similar 
to those of raising the boiling points of liquids. At the sea level 
under ordinary atmospheric pressure, water boils at 212° F., but on 
the tops of high mountains where the pressure is perhaps 25 per 
cent less, the boiling point is considerably lower. This leads to the 
well-known fact that water boils away rapidly on the mountains, 
and that things to be cooked by boiling are cooked only with 
difficulty, the reason being that sufficiently high temperatures are 
not obtainable. 

There are now definite reasons for believing that the earth is 
solid through and through, and one of them is that the earthquake 
waves are transmitted as they would be if it were a solid. The speed 
with which a wave travels through any medium, for example, the 
wave produced by striking a steel beam with a heavy hammer, 
depends upon the density of the medium and its rigidity. Earth- 



ASTRONOMY 17 

quakes are similar waves in the earth. We now have very delicate 
instruments for measuring them, even at those remote distances 
from the seat of disturbance where they have become very small. 
Suppose an earthquake starts in Japan, where many of them do start, 
and that it is of such intensity that the waves can be detected when 
they reach Europe and America. We shall suppose the time of the 
earthquake in Japan has been recorded, and that the time the wave 
reached Europe and America has also been recorded. The distance 
and the time it has taken the wave to travel from one place to the 
other being known, it is possible to compute the speed of the wave. 
Now, as has just been stated, the speed depends upon the density and 
the rigidity of the medium through which the waves pass. In the 
case of the earth the density is known, as we have shown above. 
Consequently, the only unknown is the rigidity of the earth, which 
from these observations turns out to be, on the average, considering 
the earth through and through, about that of steel. 

There are other methods of determining the rigidity of the earth, 
and they lead to the same results. One of them is the tides that the 
moon raises in the earth. It can be shown from a mathematical 
discussion of the question that if the earth had a thin crust, say 100 
miles in depth, and a fluid interior, then this crust would yield under 
the tidal force so the water on its surface would not be heaped up in 
tides. It is clear that if the crust yielded there would be no reason 
for the water to flow along it under the tidal forces. Now, it is found 
by observations that the tides are the height they should be if the 
solid part of the earth had a very high degree of rigidity. That is, the 
tidal phenomena in connection with a difficult mathematical theory 
prove that the earth is rigid when considered in its entirety. 

It was stated above that the moon's attraction on the equatorial 
bulge of the earth produced changes in its rotation. If the interior 
of the earth were fluid, so that the equatorial bulge could slip on the 
interior, then the attraction of the moon for it would produce more 
rapid changes in the motion of the interior of the earth than it would 
; f the equatorial bulge were solidly attached to the whole earth so 
that the moon would have to move all of it. It is possible to compute 
the rate of change under the hypothesis that the earth is a solid and 
also under the hypothesis that the equatorial bulge can slip on the 
interior. It is found from the actual observations that the rate of 



18 ASTRONOMY 

change is just what it should be if the earth were solid through and 
through. The conclusion to be drawn from this line of reasoning is 
that the earth is not only solid but that it has a rigidity about equal 
to that of steel. 

There are other indirect methods of treating the question and 
they all lead to the same conclusion. The fact that the earth is solid 
in the interior — when a more superficial examination of the question 
would lead to the conclusion that it is fluid — is of the highest interest. 
It is clear that this is a very important result for the geologist. It is 
interesting from the scientific point of view that we have been able 
to reach certain conclusions respecting portions of the earth which 
can never directly come under our observations. It is one of the 
triumphs of science that, through the application of laws which are 
discovered in treating material which is accessible to us, we can dis- 
cover the properties of that which is inaccessible. 

Composition of the Earth's Atmosphere. The atmosphere is 
the gaseous envelope which surrounds the earth. It is made up of 
nitrogen and oxygen and a few other substances. The thousands 
of substances which are found on and in the earth are made up of 
about eighty fundamental substances called elements. For example, 
water is a combination of the elements oxygen and hydrogen, and 
sugar is a more complicated combination of carbon, oxygen, and 
hydrogen. 

Of the earth's atmosphere about 79 per cent is nitrogen, about 
21 per cent is oxygen, and in addition there are very minute quan- 
tities of other elements such as argon, neon, and helium, and some 
compounds such as carbon dioxide and water vapor. Carbon dioxide 
is a compound made up of carbon and oxygen, and is produced by 
the combustion of coal, wood, and most other substances. 

Height of the Earth's Atmosphere. It is found upon ascending 
mountains or going up in balloons that the density of the atmosphere 
steadily decreases with increasing altitude. Numerous observations 
in various places on the earth and at various times have shown that 
at a height of three and a half miles above the surface of the earth 
the density is approximately one-half that at the surface. It is 
also found from balloon ascensions that an ascent of three and a half 
miles more reaches a place where the density of the atmosphere is 
one-half of that at the three and a half mile level, or one fourth that 



ASTRONOMY 19 

at the surface of the earth. So far as it has been possible to extend 
the observations, the density of the atmosphere is divided by two for 
every three and a half miles of ascent. If this law were indefinitely 
continued the atmosphere would, of course, have infinite extent, 
though the density would become very low after a few miles. For 
example, the density at the height of 28 miles would be only -g-i-g- that 
at the earth's surface. 

It is not possible to determine by any means whatever exactly 
where the earth's atmosphere ceases. In discussing its height we 
can refer, therefore, only to the height to which it extends in sensi- 
ble quantities. Clouds do not reach an altitude above 10 or 12 
miles, and balloons have not been sent higher than that. There- 
fore, for the purpose of carrying water vapor and balloons we 
might say its height is approximately 12 miles. But there are 
other phenomena which do not require so dense an atmosphere for 
their existence. 

A very good means of determining the height of the atmosphere 
is from the observations of meteors. These little flashes of light in 
the sky, which are commonly called shooting stars, are due to minute 
masses of matter, traveling in the interplanetary spaces, which are 
entirely invisible until they dash into the earth's atmosphere. They 
travel with very high speed, even as great as twenty or thirty miles 
per second, and the friction they encounter in striking the atmos- 
phere generates so great a heat that they become luminous. As they 
are burned up and their motion is destroyed the incandescent 
particles associated with them cool off and they become invisible. 
Now, it is possible by direct observations to find the height at which 
meteors burn. 

In Fig. 7, suppose there is an observer on the surface of the 
earth at A and another a few miles distant at B, and suppose a 
meteor strikes the atmosphere at m. The observer at A will see it 
at an angular elevation of a and the observer at B at an angular 
elevation of b. When these angles have been measured and the 
distance from A to B is known, it is possible to compute the height 
of m above the surface of the earth. The computation is made by 
trigonometry, but one can get fairly accurate results without the 
use of it. On drawing paper the distance A and B can be laid down 
to any convenient scale and the angles a and b laid oil'. The place 



20 



ASTRONOMY 



where the lines intersect will be the point m. The distance from m 
to the line AB can be measured directly by a ruler, and it can be 
found in this way how the height of a meteor is related to the dis- 




Fig. 7. 



The Height of the Meteor m Can Be Determined by 
Observations from A and B 



tance of A from B. Many observations of this sort have shown us 
that the atmosphere is sufficiently dense to an altitude of about 100 
miles to cause the meteors to burn when they strike into it. Nearly 
all of them are totally consumed before they reach an altitude of 
50 miles. 

Another phenomenon which depends upon the height of the 
atmosphere and by means of which we can compute its height is 
the twilight. 

In Fig. 8, suppose the sun is very far to the left and shines 
toward the right, its rays striking the earth in sensibly parallel lines. 
For an observer at the point P the sun is on the horizon. Suppose, 




Fig 8. An Observer at Sees the Twilight at Q Until the Sun Is 

Far Below the Horizon. From the Duration of the Twilight 

the Height of the Atmosphere Can Be Found 

for example, it is setting. For an observer at the sun has been 
down some time, depending upon the distance from to P. The 
horizon of the observer at is indicated by the line H. Now, it is 



ASTRONOMY 21 

clear from the diagram that some of the atmosphere which is above 
H, viz, that at Q, is illuminated by the rays of the sun. Conse- 
quently, the observer at 0, looking toward his western horizon, will 
see the atmosphere somewhat illuminated. It is also clear from the 
diagram that the length of time the illumination will be visible in 
the west depends upon the height of the atmosphere. The higher 
the atmosphere the longer it can be seen. Actual observation shows 
that the twilight lasts until the sun is 15 to 20 degrees below the 
horizon. When the matter is discussed mathematically this proves 
that the atmosphere is dense enough to an altitude of 40 to 60 miles 
to produce the twilight phenomena. 

Another means of determining the height of the atmosphere is 
by the aurora, a phenomenon on which is now well understood to 
be an electrical display in the rare gases of the high upper atmos- 
phere. Suppose a well-defined auroral streamer is observed from 
two places at the same time. Then, as in the case of computing 
the height of the meteor when it becomes visible, the height of the 
auroral streamer can be computed. Observations of this phenomenon 
have shown that the auroral light is visible to a height sometimes as 
great as 400 miles. 

It is seen that the various methods of determining the height 
of the observer do not agree, and the reasons for their disagreement 
are plain. They are not in harmony because each one determines 
where the atmosphere ceases to be dense enough to produce the 
particular phenomenon in question. Speaking from a practical stand- 
point, we may say that sensibly all of the earth's atmosphere is 
within 100 miles of its surface. 

In considering the mass of the earth one might at first think it 
is inappropriate to consider the atmosphere as a part of it, but upon 
a little reflection it is apparent that the atmosphere is as much a 
part of the earth as the water which covers a large part of its 
surface, or as the solid part itself. Taking into account the density 
and extent of the atmosphere, it is found that altogether it is about 
T¥oWo that of the remainder of the earth. 

Kinetic Theory of Gases. For certain discussions it is essential 
to have a clear idea of the nature of a gas. It has been stated 
above that the atmosphere is made up of a few elements and com- 
pounds in the gaseous state. These masses are composed of vast 



22 ASTRONOMY 

numbers of extremely small particles called molecules. In fact every 
substance, whether it is an element or a compound, is made up of 
small particles called molecules. When an object is in the solid state 
its molecules are fixed relatively to one another. If this were not 
so a solid body would not preserve its shape. While it is true that 
they are fixed to the extent that they do not move around among 
one another, they, nevertheless, have slight oscillatory motions. 

In the case of a liquid the molecules not only oscillate but move 
around among one another. If two liquids of the same density but 
of different colors be put together it will be seen they gradually 
mix completely because of this fact. While the molecules move 
around among one another in the case of liquids, they, nevertheless, 
do not move freely because they are so close together that each one 
is continually subject to restraints from the neighboring ones. 

In the case of a gas the molecules are far apart compared to 
their size, and they dart around in every direction with great speed. 
The collisions of the molecules are extremely frequent, but the time 
that one is sensibly influenced by another one is short relatively to 
the time between collisions. For example, if a molecule makes a 
million collisions in a second it might be that it would be sensibly 
disturbed at these collisions all together during only twottotf of 
a second. The distinction between a liquid and a gas is that in the 
liquid the molecules are continually subject to restraints from 
neighboring ones while in a gas they are most of the time free. 

The atmosphere exerts a pressure of about 15 pounds per square 
inch at the sea level. This is made evident by exhausting the air 
from a reservoir when it will be broken unless it is very strong. 
This pressure is produced by the impact of countless molecules which 
strike every square inch millions and millions of times per second. 
The individual strokes are so small and they are so frequent that 
the pressure is sensibly continuous. From the density of the 
atmosphere and the amount of pressure which it exerts, it is possible 
to compute the average speed with which the individual molecules 
move. Thus, hydrogen molecules under atmospheric pressure and at 
the freezing point move on the average with a velocity of more than 
a mile a second. The average velocity increases with the increase 
of temperature, and also with the increase of pressure. There are 
many molecules moving with velocities greater than the average, 



ASTRONOMY 23 

and many with velocities less. Theoretically there is no limit to the 
velocities with which a few may move. The higher the velocity the 
fewer the molecules which will be moving with it. 

Escape of Atmospheres. Suppose a body is projected up from 
the surface of the earth. The height to which it will rise depends 
upon the speed with which it is started. The greater the speed the 
higher it will rise, and there is a certain definite speed for which it 
will leave the earth permanently. It is found, by computation based 
upon the mathematical formulas belonging to the question, that if 
a body leaves the surface of the earth with a velocity greater than 
seven miles per second it will, except for the resistance of the 
atmosphere, leave the earth and never return. 

Now, let us apply this idea to the molecules of the atmosphere 
itself. They are darting to and fro in every direction with high 
speeds, the velocities in some cases being as great as seven miles 
per second. If a molecule is near the upper limits of the atmosphere 
where the chances of collision are growing small, and if it darts out 
away from the earth with a velocity exceeding seven miles per 
second, it will, unless it strikes another molecule, leave the earth 
permanently. In this way the earth is probably losing, molecule by 
molecule, some of its atmosphere. 

The velocities with which the molecules of the atmosphere move 
depend upon their individual weights. The lightest molecules we 
know are those of hydrogen which, as has been stated, at atmospheric 
pressure and at the freezing point move with a velocity greater than 
one mile per second. The molecules which our atmosphere is largely 
made of, viz, nitrogen and oxygen, are, respectively, 14 and 16 times 
heavier than hydrogen and move on the average with about one- 
fourth the velocity of hydrogen. This velocity is so far below the 
seven miles per second necessary for escape from the earth that it 
is clear there is no great danger of the atmosphere escaping rapidly. 
Nevertheless, there is indefinite time available for its escape and 
there might be a danger of its being seriously depleted in this 
manner. 

Before drawing definitely the conclusion that the earth is losing 
its atmosphere and that it is continually becoming more tenuous, 
we should see whether there are not some ways in which it is being 
restored. One of the ways in which the earth's atmosphere is 



24 ASTRONOMY 

increased is by the escape of gases from the earth itself, particularly 
from volcanoes and hot springs. But perhaps the escape of gases 
from the rocks as they are dissolved by the action of the water and 
air is equally important, for it is found that almost all the rocks of 
the earth's surface contain in their interstices large quantities of gas, 
which is called occluded gas. 

There is another way in which the earth's atmosphere is prob- 
ably to some extent replenished. It was remarked above that 
meteors strike into the earth's atmosphere and are burned up by 
friction with it. When a body is burned up the material of which it 
is composed is not utterly destroyed but is only changed in form. 
For example, when wood is burned the carbon in it unites with 
the oxygen of the air and produces carbon dioxide, which goes 
off as a gas. Some of the mineral substances remain behind in the 
ashes. The vapors given off in the process of combustion and 
the ashes left behind together equal the total quantity of matter in the 
original wood plus the oxygen added to it during the combustion. 
Therefore, when meteors strike into our atmosphere and are burned, 
the product of the combustion is added to the earth. If it is solid 
it slowly settles to the earth, and if it is gaseous it becomes a part 
of the atmosphere. The amount of atmosphere added in this manner 
in a year is, of course, small, but it may be sufficient to make up 
for that which is lost. 

It is probable, also, that the region in the neighborhood of the 
sun through which the earth moves is rilled sparsely with wandering 
molecules. They may have been lost from the earth and other 
planets, or may never yet have been gathered into any large body. 
If this is true the earth in its course around the sun would gradually 
gather them up and in this manner replenish its atmosphere. 

It is clear from what has been said that there are ways in which 
the earth loses its atmosphere and others in which it tends to gain 
one. There is no astronomical means of determining whether the 
loss is greater than the gain or not. Probably the gain and loss have 
reached a state of equilibrium. If the earth had a very extensive 
atmosphere, so that its borders were farther from its surface it would 
lose it more easily and consequently more rapidly, while it would 
gain only a little more than now. If it ever had so large an atmos- 
phere that it was lost faster than it was restored, probably enough of 



ASTRONOMY 25 

it has been lost so that it is now in approximate equilibrium. It is 
somewhat analogous to the condition of a body of water subject to 
evaporation. An exposed vessel of water continually loses particles 
by their leaping into the atmosphere. It also continually gains them 
by those which are in the atmosphere plunging into it. If the atmos- 
phere is initially very dry, then the evaporation is more rapid than 
the restoration of water from the air. But as evaporation goes on, 
if the atmosphere above the vessel of water is enclosed, after a time 
a state of equilibrium is reached in which the loss and gain are exactly 
equal. Probably in a somewhat analogous fashion the condition of 
the earth's atmosphere, respecting its loss into space and the gain 
from the various possible sources, has reached a state of equilibrium. 

It was stated above that in order for a molecule to escape from the 
earth it must leave its surface with a velocity of approximately seven 
miles per second. If the earth were smaller or less dense it would have 
a smaller gravitative power and a molecule could escape by leaving 
at a somewhat lesser velocity. The moon is an example of a smaller 
world where it is easier for molecules to escape. The diameter of the 
moon is about one-fourth that of the earth and its mass about one- 
eightieth. If a body leaves its surface with a speed of 1.5 miles 
per second it will permanently escape. It is a significant fact in 
this connection that the moon has no sensible atmosphere. 

On the other hand, bodies which are larger than the earth have 
greater gravitative power and higher velocities of escape. In the 
case of the great planet Jupiter, which is nearly 1,000 times as big 
as the earth and has a mass more than 300 times as great, a body 
must leave its surface with a velocity of over 37 miles per second in 
order to escape. It is clear from this that it can control a much 
greater atmosphere than the earth can; and this theory is in har- 
mony with the observed fact that Jupiter has a great atmosphere. 
In the solar system the greatest body is the sun, and the computa- 
tion shows that a particle must leave its surface at the rate of 380 
miles per second in order to permanently escape. Obviously, there 
is small chance for the particles of an atmosphere to escape from 
its control, and observation shows that it has a greater atmosphere 
than any other member of our system. 

Effects of Atmosphere on Climate. Aside from the sun the 
atmosphere is the most important influence affecting our climate. 



26 ASTRONOMY 

In the daytime, when the earth is subject to the direct rays of the 
sun, the atmosphere absorbs a considerable part of them and keeps 
the temperature from rising to the point it would otherwise reach. 
It is difficult to determine what part of the sun's radiation is absorbed 
in the atmosphere, but certain computations make it as high as 50 
per cent. The effectiveness of the atmosphere in absorbing the sun's 
heat is noticed when one ascends a high mountain or even lives on 
an elevated plateau. In those exposed places the sun's radiation 
is noticeably more intense than at the lower levels. Therefore, one 
effect of the atmosphere is to keep down the temperature during 
the middle of the day. If the atmosphere absorbs a certain amount 
of the light and heat coming from the sun, it is not entirely lost to 
the surface of the earth because the atmosphere later radiates this 
heat again. Part of it is radiated out into space and part of it toward 
the earth. That is, some of the heat which comes from the sun is 
caught in the earth's atmosphere in the daytime and held there a 
while and delivered to the earth's surface by radiation at night. 
In this way the earth's atmosphere makes the surface of the earth 
warmer at night than it would otherwise be. 

Another effect of the atmosphere is that it prevents radiation 
from the surface of the earth at night. Though the rays are not 
visible the earth radiates heat out into space as a luminous body 
radiates light. The atmosphere above the surface of the earth catches 
a part of this radiated heat and in turn radiates it again. A part of 
it, of course, comes back to the earth. It is a matter of common 
observation that the nights are very cool in the high altitudes, and 
the explanation is simply that the atmosphere there is so tenuous 
that it does not catch the heat which the earth is radiating. There- 
fore, considering the 24 hours, it is seen that the effect of the atmos- 
phere is to reduce the variations in temperature. 

There is another important way in which the atmosphere tends 
to equalize temperatures. The equatorial part of the earth receives 
much more light and heat than the high latitudes and this sets up 
great currents in the atmosphere. In the northern hemisphere the 
atmospheric currents are on the whole from the southwest toward 
the northeast. The point is that the atmosphere moves from the 
heated equatorial regions toward the frozen regions of the north. 
In this manner enormous quantities of heat are carried from regions 



ASTRONOMY 27 

where they are not needed to regions where otherwise it would be 
very cold. The effects are seen on the western coasts of the large 
land areas in the northern hemisphere, which in all instances have 
much warmer climates than corresponding latitudes on the eastern 
shores. It is clearly not because the western shores receive more 
heat from the sun, but because they are warmed by heat which fell 
on the earth elsewhere. Now, it is impossible for the atmosphere 
to go northward in the northern hemisphere without an equal amount 
going southward. The warm currents pass along the surface of 
the earth carrying the mild temperature into higher latitudes, 
and the cool air from the polar regions goes southward and reduces 
the temperature in the equatorial zone. In this manner the tempera- 
ture at the surface of the earth considered as a whole is much more 
uniform than it would be except for the atmosphere. 

The effects of the atmosphere on the climate depend to some 
extent upon its constitution. This is clearly seen to be so by con- 
sidering the difference in temperatures when it is clear and cloudy. 
The gardener does not fear a frost on a cloudy night because he 
knows the clouds keep in the radiations from the earth and prevent 
the temperature sinking below the freezing point. On the other 
hand, when the atmosphere is clear and relatively free from water 
vapor it is more transparent to the radiations from the earth and 
the temperature falls more quickly and to a lower point. 

Water vapor is not the only substance of the atmosphere which 
has the property of strongly absorbing light and heat. Another 
compound which is important in this respect is carbon dioxide. 
Though the amount of this substance is small in the earth's atmos- 
phere it is probably important in absorbing the solar radiation. If 
the amount were considerably increased the mean temperature of 
the earth would rise, and if it were considerably decreased it would 
fall. This is an interesting point in connection with the fact which 
geologists have worked out for us, namely, that the climate of the 
earth has alternately been much warmer and colder than it is at the 
present time. The northern part of the United States has time after 
time been visited by great ice sheets which have pushed down from 
the North, and which show that at certain epochs the mean tem- 
perature has been much lower than it is at present. On the other 
hand, in mtervening epochs the temperature has been higher, for 



28 ASTRONOMY 

in these altitudes and even so far north as Greenland semi-tropical 
plants have flourished. It may be that these oscillations in tem- 
perature are not due at all to astronomical causes but only to the 
varying composition of the earth's atmosphere. There are reasons 
for believing that for long periods the amount of carbon dioxide will 
decrease as it becomes locked up in coal beds and absorbed by the 
oceans, and that then for long periods it will increase. This change 
may be sufficient to cause all the climatic changes of which we have 
evidence. It is generally supposed that at the present time the 
amount of carbon dioxide in the atmosphere is slowly increasing and 
that the climate is getting slightly warmer. It should not be under- 
stood, however, that the change is rapid enough so that it can be 
observed for so short a time as a thousand years. Those changes 
which are observed, or which are supposed to have been observed, 
are almost certainly of a local and more temporary character. 

It follows from this discussion that if one is to consider the 
question of the habitability of another world, the question of the 
extent and nature of its atmosphere is a very important one. In 
the first place, a definite constitution of the atmosphere is neces- 
sary for most of such life processes as take place upon the earth, 
and in the second place the climatic effects are sa important that 
they may be the determining factor. 

Refraction of Light by the Atmosphere. If light passes obliquely 
from a rarer medium into a denser medium, its direction changes 
slightly at the surface separating the two, the amount of change 
depending upon the differences of densities and to some extent upon 
the constitution of the two media. When the light from a celestial 
object enters our atmosphere from vacant space its direction is some- 
what changed. In this case it does not pass from one medium into 
another of constant density, but as it passes down through our atmos- 
phere it gets into a medium whose density continuously increases, 
Consequently, the path of the ray of light continually changes. 

In Fig. 9, suppose the ray of light comes from a star S and 
strikes the atmosphere at the point A. At this point its direction 
begins to change and continually changes until it reaches the sur- 
face of the earth at 0. An observer at sees the star in the direc- 
tion from which the light came when it entered his eye; that is, the 
star seems to him to be at S'. Since the star is at a distance which 



ASTRONOMY 29 

is sensibly infinite it is actually in the direction OL. Of course, in 
the diagram the difference in direction is greatly exaggerated. The 
point to be noticed is that the star appears to be higher in the sky 
than it actually is. 

This change of direction, or atmospheric refraction, is zero for 
a star at the zenith, and increases continuously until the horizon is 
reached. At the horizon it is a little over one-half a degree, the 
exact amount depending upon several factors such as the density of 
the air at the time, i. e., the barometric pressure, the temperature, 
and upon the amount of water vapor it contains. 

One of the consequences of the refraction of light is that an 
object (for example, the sun) apparently rises before it actually is 
above the horizon, and apparently does not set until after it is actually 
below the horizon. That is, the sun is apparently above the horizon 
longer than it would be except for the refraction. One might infer 




Fig. 9. The Light from the Star S Is Rent as It Comes through the 
Earth's Atmosphere so That It Seems to Be in the Direction 5' 

from this that we get more light and heat from the sun than we would 
if it were not for the atmosphere. But the absorption by the atmos- 
phere of the sun's light and heat more than offsets this slight gain. 

There is another interesting consequence of the fact that the 
refraction increases to the horizon. When the sun or moon is on 
the horizon, light from the upper part is refracted less than the 
light from the lower part. The lower part being apparently lifted 
more than the higher part makes it appear flattened in the vertical 
direction, as illustrated in the case of the sun, Fig. 10. This is often 
enough to be very conspicuous, and if it has not been observed it 
should be looked for. 

In making astronomical observations it is often important to 
locate the exact position of the object. Now, it has just been seen 
that the apparent position is different from the exact position on 
account of refraction. Consequently, it is necessary to make cor- 



30 



ASTRONOMY 



rections to the direct observations for this refraction. An example 
of where this is important is in making observations at sea for deter- 
mining the position of a ship. The correction would be rather simple 
if it were not for the fact that the refraction varies with the state of 
the atmosphere. This introduces uncertainties which are important 
when the object under observation is near the horizon. In the mos*t 
exact kind of astronomical work it is important that the observation 
should be taken when the object viewed is not far from the zenith, 
and this condition is always secured if possible. 







Fig. 10. The Refraction of Light Makes the Sun Appear Flattened 
When It Is Seen on the Horizon 

The atmosphere is not only of variable density from the highest 
regions to the surface of the earth, but there are waves in it which 
cause the density at a given point continually to vary. This makes 
constant changes in the refraction of light, though, of course, of no 
great extent. One of the consequences of this varying refraction 
is seen best in observations of the stars. On a clear night, especially 
in the winter time, and particularly if it is not calm, the stars are 
seen to twinkle or scintillate. This twinkling is due entirely to the 
fact that the light from the stars is passing through an atmosphere 
whose density is constantly changing so that the refraction is 
unsteady. It is easy to verify the fact that the twinkling is greater 
the nearer the star is to the horizon. 

Relative Rotation of the Earth. The most casual observer of 
the heavenly bodies knows that the stars rise in the east, pass across 
the sky, and set in the west, just as the sun and moon do. This 
refers to those which are not near the pole of the sky. Any observer 



ASTRONOMY 31 

of the stars can see that those which are near the pole of the sky 
go around it in circles whose centers are very close to the pole star. 
For example, if the Big Dipper is on the east side of the pole in the 
evening it will pass in a circle around above it during the night and 
be on the west side in the morning. If one knows where it is in the 
evening he can tell the time of night, at least approximately, by 
observing its position. '• 




Fig. 11. Circumpolar Star Trails Photographed at the Yerkes Observatory- 
Fig. 11 shows the trails of the stars in the vicinity of the pole 
as they were photographed during an exposure of a little more 
than an hour with the telescope pointed to the northern sky and 
kept fixed. The conspicuous streak below the center and a little 
to the left is the trail of the pole star itself, which is thus shown to 
be not exactly at the pole of the sky. Most of the stars whose 
trails are shown are invisible to the unaided eye. 



32 ASTRONOMY 

Since all heavenly bodies rise in the east (except those so near 
the pole they simply go round it), travel across the sky, and set in 
the west to reappear again in the east, it follows that either they go 
around the earth from east to west or the earth turns from west to 
east. So far as these simple observations go it is not possible to deter- 
mine which of the two theories is correct. It is incorrect to suppose 
that those ancients who believed that the earth is fixed and the sky 
goes around it adopted any theory which violates the common facts 
of observation. This theory is as much in harmony with the apparent 
motions of the heavenly bodies as the one we have, viz, that the 
stars are fixed and that the earth turns from west to east. It has 
already been remarked that one of the characteristics of science is 
that it gives reasons for its conclusions. Therefore, it will be necessary 
to take up and explain the reasons we have for believing that the 
earth moves and that the sky is fixed. Before taking up the question 
of the motions of the earth in particular, we shall consider the laws 
of motion of bodies in general. 

Laws of Motion. The laws of nature are in an important respect 
different from civil laws, and it is to some extent unfortunate that 
the same term is used. A civil law prescribes a mode of conduct 
and penalties if it is violated. A civil law can be broken at will if 
one is willing to accept the penalty, or at least the chance of it. A 
natural law, or a law of nature, on the other hand, does not pre- 
scribe anything, but is a statement of the way all phenomena of 
a certain class proceed. If it is a true law of nature it describes 
the way phenomena invariably proceed and there are no exceptions 
to it. 

The laws of motion are statements of the way bodies actually 
move. They were first given in their completeness by Newton in the 
Principia in 1686, although they were to some extent understood by 
his predecessor Galileo. They were called by Newton axioms, 
although they can hardly be said to be axioms in the ordinary sense 
of the term, since for thousands of years men believed motions 
were different from what they are as expressed by these laws. The 
laws, essentially as Newton gave them, are: 

Law I. Every body continues in its state of rest or of uniform 
motion in a straight line unless it is compelled to change that state by 
exterior forces acting upon it. 



ASTRONOMY 33 

Law II. The rate of change of motion is proportional to the force 
impressed and the change takes place in the direction of the straight 
line in which the force acts. 

Law III. To every action there is an equal and opposite reaction; 
or, mutual actions of bodies are always equal and oppositely directed. 

The importance of these laws can be understood from the fact 
that every astronomical phenomenon involving the motion of matter, 
and . everything upon the earth involving the motion of matter, is 
interpreted by using them as a basis. A little reflection will show 
that there are few things, indeed, which are not associated with the 
motion of matter. Even the process of thinking is probably asso- 
ciated with the motion of matter in the changing structure of the 
brain. Because of the wide application of these laws it is necessary 
to give them careful attention. 

The first law states the important fact that if a body is at rest 
it will never begin to move unless some force acts upon it, and if 
it is in motion it will forever move at uniform speed in a straight 
line unless some exterior force acts upon it. This in two respects is 
opposite to the views held generally before the time of Newton. In 
the first place, it was supposed that bodies would descend without 
forces acting upon them. In the second place, it was supposed that 
if a body were in motion it would stop unless some force were con- 
tinually applied to keep it going. These errors prevented the prede- 
cessors of Newton getting any satisfactory explanation of the motions 
of the heavenly bodies. 

The second law means by the "rate of change of motion" the 
product of the mass and the rate of change of velocity. It might 
be made to read, the rate of change of velocity is proportional to the 
force impressed and inversely proportional to the mass moved, and 
the change takes place in the direction of the straight line in which 
the force acts. The first two laws consider a single body subject to 
exterior forces. 

The third law expresses the way in which two bodies act on 
each other. It means essentially that no body can change the state 
of the motion of another body without having its own motion cor- 
respondingly changed, and this is equally true whether the bodies 
are in actual contact or connected by some invisible bond oi force 
such as gravitation. The difficulties in getting a clear mental picture 



34 ASTRONOMY 

of this law come largely from the fact that it is not possible to get 
two bodies subject only to their mutual interactions. If a man and 
a small boy pull in opposite directions on a rope, the man pulls the 
boy, and it seems that the law is violated. The reason of the apparent 
violation of it is due to the fact that there are other forces in operation, 
particularly the friction of the feet of the man and the boy with the 
ground. If they were both in small boats on the water, then each 
would move with a speed inversely proportional to his mass. It 
follows from this fact, which we shall suppose is verified in experi- 
ment, and the second law of motion, that the forces are equal and 
opposite. The more nearly the exterior forces are eliminated the 
more nearly the law is verified. It is to be understood that the laws 
of motion can be verified with a high degree of precision in the labora- 
tory. They have been tested in this manner thousands of times and 
no deviations from them have been observed that can not be explained 
by extraneous forces which it was not possible to eliminate. They 
have also been verified indirectly in thousands of ways, and some of 
these verifications, particularly in astronomy, are more exact than 
any of a direct character. Just as railway trains obey the laws of 
motion and in consequence would jump the track on curves if the 
outside rails were not elevated, so also the heavenly bodies in 
their motions obey the laws. But in the case of heavenly bodies the 
disturbing factors are almost entirely absent, and the operation of 
the laws is observed under almost ideal conditions. 

Rotation of the Earth Proved by Eastward Deviation of Falling 
Bodies. If the earth rotates, then the farther a body is from its axis 
the faster it goes. The circumference of the earth at the equator is 
about 25,000 miles, so that a body on the surface of the earth at the 
equator moves eastward if the earth rotates at the rate of about 
1,000 miles an hour. 

In Fig. 12, suppose that C is a point on the axis of the earth 
and that CP is a line perpendicular to it. Suppose is the top of a 
high tower whose base is at P (of course, the height of the tower is 
greatly exaggerated in the figure), and suppose the earth rotates in 
the direction PP' and that the line CP moves to CP' in one unit of 
time. Therefore, a mass at the bottom of the tower has the velocity 
PP'. Now, consider a body at the top of the tower whose velocity 
is 00' '. When the body is dropped its motion will be the resultant 



ASTRONOMY 35 

of its motion toward 0' and of the attraction of the earth for it toward 
C. This attraction is at right angles to the line 00' and will, there- 
fore, not diminish the velocity in this direction. Hence, in the unit of 
time the body will move precisely as far eastward as though it were 
not falling. Since the earth's attraction acts continuously it will fall 
faster and faster until it strikes the surface of the earth. The curve 
described by the body will be OQ, Q being the point where it strikes 
the earth. This point will be east of the foot of the tower P' at 
the time it strikes the surface because the distance 00' is greater 
than PP'. Therefore, the falling body will have an eastward devia- 
tion. On the other hand, if the earth were not rotating it would 
strike at the foot of the tower. 

From this discussion we see how the 
body will fall if the earth rotates and how 
it will fall if it does not. The experiment 
will decide the matter. The problem is 
one of some practical difficulty because 
very slight air currents will cause enough 
change in motion to mask the small east- 
ward deviation, which in our latitude 
amounts to only about an inch in a fall 
of five hundred feet. The most successful 
experiments have been carried out in mine ««,„„--, * w . 

r Fig. 12. The Eastward Devia- 

shafts where large falls can be secured and ^L^tSf K? Ewth 8 
where by covering them the air currents 

can be destroyed. The experiments have actually shown the east- 
ward deviation, and therefore have proved the eastward rotation of 
the earth. 

Rotation of the Earth Proved by Its Shape. It follows from the 
laws of motion stated above, and the law of gravitation, that if the 
earth does not rotate it will be exactly spherical except *f or slight 
irregularities due to its lack of homogeneity. It also follows from 
the laws of motion that if it is rotating it will be bulged at the equa- 
tor and flattened at the poles. The first law of motion asserts 
that a body subject to no forces will move in a straight line. 
Now, the particles at the earth's surface, especially at the equator, 
tend to move in a straight line in harmony with this law, and are 
held to the earth only by its attraction. This tendency to move 




36 



ASTRONOMY 



out in straight lines produces the equatorial bulge. If the earth 
moved seventeen times as fast as it does now and were of the same 
size and shape, a loose particle on its surface at the equator would fly 
away into space. 

It is seen that if the earth did not rotate it would be round, and 
that if it did rotate it would be oblate. The observations again must 
settle the question as to which is true. As was explained above, 
measurements of arcs on the surface of the earth have shown con- 
clusively that the earth is bulged at the equator and flattened at 
the poles. Therefore, we are forced to the conclusion that the 
earth rotates. This method of proving its rotation gives us the 
position of its axis but does not determine for us which way it 

moves. 

Rotation of the Earth Proved by Fou= 
cault's Pendulum Experiment. It follows 
from the laws of motion that a pendulum 
set swinging tends to move continually in 
the same plane. Let us imagine a pen- 
dulum suspended from A, Fig. 13, over 
the exact pole of the earth, and suppose 
that it is started swinging in the plane of 
the meridian m. If it is subject to no 
other force than the attraction of the earth, 
which is directed toward the earth's center, 
it will continually swing in this plane. Let us suppose that the earth 
is rotating toward the east, the direction being indicated by the arrow 
on the equator in Fig. 13. The meridian m will turn in the direction 
of the arrow while the pendulum stays fixed. If an observer were on 
the earth at the pole the earth would, of course, seem to him fixed 
as it does to us where we live, but the pendulum would seem to him 
to be turning in the westward direction. If he should watch it for 
24 hours he would find that it made a complete apparent revolution 
in that time. 

If the pendulum were suspended at the equator instead of at 
the pole there would be no more tendency for it to rotate in one 
direction than the other, and, as can be easily seen, it would not 
change the apparent plane of its vibration. Therefore, an observer 
there would notice no rotation of the pendulum. 




Fig. 13. Proof of Earth's Rota- 
tion by Foucault Pendulum 



ASTRONOMY 37 

Now, consider a point between the pole and the equator. At 
the pole the plane of the pendulum's motion rotates in 24 hours and 
at the equator it does not rotate 'at all. In the intermediate latitude 
it rotates but the period is longer than 24 hours, its length depending 
upon the latitude. In our latitude the period of apparent rotation is 
about 36 hours. 

It follows from this discussion that if a pendulum is set swing- 
ing in our latitude, the plane of it apparently slowly deviates to the 
west if the earth rotates to the east. On the other hand, if the earth 
is fixed, it will continually swing in the same plane. The experiment 
must be made in order to prove which theory is correct. This very 
ingenious and convincing method of proving the rotation of the 
earth was devised and carried out by Foucault, in Paris, in 1851. 
He suspended a heavy iron ball by a steel wire about 200 feet in 
length. It was pulled to one side of its lowest point and fastened by 
a thread and left until it came perfectly to rest. Then the thread 
was burned so as not to give it any sidewise disturbance, and it 
began to swing. Underneath it the floor was marked so that the 
direction of its swing could be seen easily. It was observed then that 
hour after hour it apparently deviated to the west, which meant, 
of course, that the earth was turning to the east under it. This 
experiment can be easily performed in space where a shaft of con- 
siderable length, free from disturbances, can be secured. In carry- 
ing out the experiment it is necessary to be careful to start the 
pendulum swinging in an exact plane, for if it has a slight elliptical 
motion it will perform a rotation independent of that produced by 
the actual motion of the earth. Since this experiment has been 
many times performed and has always shown a westward apparent 
deviation in harmony with the theory, we must conclude also from 
this line of evidence that the earth rotates eastward. 

Analogy with Other Heavenly Bodies. It is found from observa- 
tions which do not depend upon the theory that the earth rotates or 
does not rotate, that many of the other heavenly bodies are com- 
parable to the earth in size. The moon and some of the planets 
are smaller; Venus is about the size of the earth; Jupiter is about 
one thousand times greater; and the sun about a million times greater. 
Our modern powerful telescopes show markings on many of these 
objects of such a character that it can be determined whether they 



38 ASTRONOMY 

rotate or not. It is found that all of them on which markings can 
be observed turn on their axes, and what is a remarkable fact, in the 
same direction. The periods of their rotation vary considerably. 
For example, that of the moon is 27| days, Jupiter about 10 hours, 
and the sun about 25 days. But the essential point of interest here 
is that these other bodies, which are in most essential respects similar 
to the earth, some being smaller and some larger, all rotate. It is 
not reasonable, therefore, to suppose that the earth is the one excep- 
tion. Hence, we should conclude from this alone that the earth 
does rotate, though this proof is by no means so conclusive as the 
proofs given above. 

Uniformity of the Earth's Rotation. It follows from the laws 
of motion, and in particular from the first law, that if the earth 
were subject to no external forces and were fixed in size and shape, 
it would rotate on its axis with absolute uniformity. One might 
suppose the matter could be tested by comparing it with clocks. 
But as a matter of fact all the clocks which have been made, and 
which probably can be made, run w T ith so much greater irregularity 
than the earth rotates that no test of this character can succeed . 
In fact, the rotation of the earth is used to check the running of 
clocks and to regulate them when they depart from perfect adjust- 
ment. 

One might test the rotation of the earth by comparing it with 
some other celestial phenomenon which is known to proceed uni- 
formly. There are, however, no such phenomena. Probably the 
earth is as good a measurer of time as anything which can be observed. 
The best we can do is to discuss those forces and changes which have 
a tendency to change its rate of rotation. 

The earth is rotating in the luminous ether and a considerable 
quantity of meteoric matter. The latter, if not the former, has a 
tendency to retard its rotation and consequently to make the day 
a little longer. But this resistance is exceedingly small and certainly 
does not lengthen the day by a second in 1,000,000 years. 

The moon and sun generate tides in the earth which on the 
whole move around it in a westerly direction, because these bodies 
in their apparent motions move to the westward. The tides, there- 
fore, on the whole, beat in upon the eastern shores and act as a break 
on the rotation of the earth. While there can be no doubt whatever 



ASTRONOMY 39 

that the tides slow up the rotation of the earth to some extent, the 
amount of the retardation is probably so small as to be of no impor- 
tance whatever. It is not possible to measure it with any degree of 
exactness, but it is not likely that the earth's day increases in length 
from this cause one second in 500,000 years. 

The interior of the earth is hot and it is gradually losing heat 
by conduction to the surface and radiation into space. As it loses 
heat it probably shrinks a little. If a rotating body shrinks it rotates 
faster. The principle upon which this statement is based, which is 
a conclusion drawn from the laws of motion, is that in a rotating 
body subject to no exterior forces the whole quantity of rotation is 
a constant. By quantity of rotation is meant the mass multiplied 
by the velocity multiplied by the distance from the axis of rotation. 
Therefore, if a body shrinks so that the distance of each mass in it 
from the axis of rotation becomes less, the velocity must be increased 
in order to restore the equality. Theoretically this effect would lead 
to a shortening of the day. But the earth's contraction, because of heat 
losses, is so slow that probably the length of the day is not dimin- 
ished in this way by so much as one second in twenty million years. 

There are certain other causes besides its shrinking which change 
the distance of matter from its axis of rotation. For example, if a 
river runs from high latitudes to low latitudes, as the Mississippi, 
and if it carries sediment in its waters and deposits it in low latitudes, 
by this process matter is taken from a certain distance from the 
earth's axis and left at a greater distance from it. So far as this factor 
is concerned, the earth is to some extent retarded in its rotation. 
Not all rivers, however, run toward the equator and those flowing 
in the opposite direction offset this. The evaporation of water in 
equatorial regions and its deposit as snow in the higher latitudes is 
a factor working in the other direction and there are, also; many rela- 
tively minute surface changes, some acting one way and some another. 

Some of the causes which have been enumerated above tend 
to increase the rate of rotation and others to decrease it. It is not 
possible to determine at the present time whether, on the whole, 
the day is becoming longer or shorter. The only thing certain about 
it is that the rate of change is exceedingly slow and will not produce 
sensible results before millions of years have elapsed. This is a 
question of some practical interest because if the day should become 



40 



ASTRONOMY 



very much longer, say forty hours in length, the temperature in our 
latitudes would fall so low nearly every night in the year that there 
would be killing frosts. Again, in the correspondingly longer day the 
temperature would rise higher than under present conditions. 

Variation of Latitude. In the preceding paragraph the discussion 
referred to the possible change of the rate of rotation of the 




5"«£T«£S 



Fig. 14. The Path of the Earth's Pole from 1900 to 1908 



earth on its axis. The question before us now is whether 
the earth continually rotates around some fixed axis. It has 
sometimes been supposed by those not familiar with the dynamics 
of the question that the former warm temperatures in the high 
latitudes and the cold temperatures in the low latitudes might 
be accounted for by a change in the position of the axis of the 
earth. It is not dynamically impossible that the axis of rota- 



ASTRONOMY 41 

tion should change, but if it does change it would be in the nature 
of an oscillation around some mean position. That is, the earth 
might have a sort of wabbling motion, just as a top has when it is 
not running steadily. Observations made for the purpose of detect- 
ing wabbling did not succeed until about thirty years ago. The 
reason of the failure was that the amount of deviation was exceedingly 
minute. This wrbbling is spoken of as the variation of latitude, 
or the variation of the position of the pole, the movements covering 
a territory about 60 feet in diameter, Fig. 14. 

If a top is running so steadily that it "sleeps" it will run per- 
manently in that condition unless disturbed by some exterior force. 
As a matter of fact, there are many exterior forces always operating 
on the top. Similarly, if the earth were rotating around the axis 
of its figure it would forever run that way unless it were disturbed 
by external forces, or by some redistribution of its own mass. As 
has been stated, there is a slight wabbling and the question at once 
arises as to what are the causes which have produced it. At the 
present time they are not known. There are many things which 
have some influence upon it, such as the varying wind and ocean 
currents during the year, and the deposition of snow in the high 
latitudes. Also the attractions of the moon and sun on the equa- 
torial bulge may have some effect. 

The nature of the causes is indicated to some extent by the char- 
acter of the wabbling. If the earth were not disturbed it would 
wabble in a perfectly definite fashion, depending upon its mass, size, 
shape, and rate of rotation, and would forever continue to wabble 
in this fashion if it were perfectly rigid. The period of this wabbling 
is also a perfectly definite quantity. The observations have shown 
that the wabbling is of a complicated character, being really the 
result of two separate motions. One has a period of one year, and 
the other of about 430 days. The yearly period is not the natural 
one for the earth's wabbling and consequently this irregularity 
must be produced by a continually acting force whose period of 
change is one year. The other irregularity is that one which the earth 
would have if it were left entirely free from external disturbances. 
Now, 430 days is not the period the earth's wabbling would have if 
it were absolutely rigid. If it were a perfect solid, yielding to no 
forces however great, its period of wabbling would be about 305 



42 ASTRONOMY 

days. But if its rigidity were only that of steel, which must be con- 
sidered highly elastic in treating of so great a mass as the earth, 
then its period of wabbling would be about 440 days, which is near 
that actually observed. It follows from this that the rigidity of the 
earth is between that of the perfectly unyielding solid and that of 
steel, and that it is near that of steel. Therefore, we have here a 
new proof that the rigidity of the earth, when considered through 
and through, is about that of steel. 

Apparent Motion of the Sun with Respect to the Stars. The 
rising and the setting of the sun are such conspicuous phenomena 
that the most careless observer understands them well. But it is not 

so well known that the sun has 
a motion among the stars. It 
moves eastward about as the 
moon does, only less rapidly. 
Nearly everyone has noticed the 
fact that the moon moves day by 
day eastward among the stars. 
The reason the phenomenon is 
not noticed in the case of the sun 
is that the stars can not be seen 
in its immediate vicinity. But 
indirectly, the fact can be easily 

Fig. 15. The Sun Would Have an Apparent .. . . . 

Eastward Motion If the Earth Were Fixed established and Was Well KnOWn 

with the Sun Moving Around It 

in remote antiquity. 
Suppose a certain group of stars is on the meridian at midnight 
when the sun is exactly opposite. That is, if one starts at the sun and 
goes eastward along the sky until he gets to the stars he finds them 
at a distance of 180 degrees. Suppose that after a month the same 
group of stars is found 30 degrees west of the meridian at midnight. 
In this case, starting from the sun and going eastward along the sky 
to the stars, he has to go a distance of 180° — 30°, or 150°. Since it is 
now 150 degrees from the sun to these stars, while a month before 
it was 180 degrees, it means that the sun has gone eastward among 
them 30 degrees. Just such facts as these are actually established 
by the observations. Every month in the year the sun goes east- 
ward among the stars 30 degrees. It can be indirectly established, 
as has just been explained, and more directly by the use of large tele- 




ASTRONOMY 



43 



scopes which will show the brightest stars fairly close to the sun. Hence 
the question of the explanation of this phenomenon arises. 

In Fig. 15, suppose E represents the earth which is fixed except 
for its rotation which was proved above. Suppose the sun moves 
around the earth in the curve SiS 2 S s Si. When it is at the point Si it 
is opposite the stars at s z and in the direction of the stars at s v 
The stars at s 3 are visible on the meridian at midnight and those at 
s x can be seen only with a telescope. Counting in the direction of 
motion from s x to s s the distance is found to be 180 degrees. In a 
month suppose the sun is at *S 2 . Then the stars at s 3 are 30 degrees 
west of the meridian at midnight and those at s 2 are in the direction 
of the sun and can be seen only 
with a telescope. Now, the dis- 
tance from s 2 forward in the di- 
rection of the sun's motion to s 3 
is 150 degrees. As the sun pro- 
ceeds around the earth it is suc- 
cessively seen in all directions 
from the earth. This is in perfect 
harmony with the facts of obser- 
vation as recorded above. Con- 
sequently, it is easy to see why 
the ancients were satisfied with 
the theory that the earth is the 
center of the universe, since they 
had only those observations which we have mentioned, and which 
have just been shown to be in harmony with this theory. 

Now, suppose S, in Fig. 16, represents the sun, and that the 
earth moves around it in the curve E X E 2 E Z E^. When the earth is 
at E l the sun is in the direction of the stars at Sy Suppose the earth 
moves forward in its orbit to E 2 in one month. The sun then appears 
to be among the stars at s 2 , and as the earth moves forward in its 
orbit the sun apparently moves forward among the stars and com- 
pletes a circuit of the heavens, while the earth goes around the sun. 
It is seen that the apparent motion of the sun in this case is exactly 
the same as that when the earth was supposed to be fixed at the 
center and the sun to go around it. This theory is therefore in as 
perfect harmony with the ordinary observations of the apparent 




Fig. 16. The Motion of the Earth around 
the Sun Causes It Apparently to Move 
Eastward among the Stars 



44 ASTRONOMY 

motion of the sun as the preceding, and the ancients might have 
adopted it as well as the other. As a matter of fact, the heliocentric 
theory, as this is called, was advanced by the ancient Greeks. How- 
ever, it is clear from this discussion that the facts furnished by obser- 
vations of the apparent motion of the sun are not sufficient to enable 
us to decide which of the two theories is the correct one. 

The proofs that the sun is the center and that the earth revolves 
around it will be gone into with some care. This was a subject of 
bitter discussion for- many centuries, but the matter was settled 
three hundred years ago in the days of Copernicus and Galileo, and 
has been open to no question whatever since the time of Newton. 
The first modern astronomer to develop definitely the heliocentric 
theory and to attempt to work out the motions of the heavenly 
bodies and in particular the sun upon it, was Copernicus (1473-1543). 
It is to be understood that not only is the motion of the sun to be 
explained, but the motion of the planets with respect to it, and this 
complicates the question greatly. Copernicus succeeded in showing 
that the heliocentric theory is in harmony with all the observed 
motions of his time, and he drew the conclusion that this is the cor- 
rect theory since it is more reasonable than that the relatively small 
earth is the center for the motions of all the great bodies, especially 
for that of the sun. He did not have what we would now regard as 
a strict proof of the correctness of this theory. 

Revolution of the Earth Proved by the Parallax of the Stars. 
Let us suppose that the stars are fixed objects in the heavens. 
Then, if the earth is the center and the sun goes around it, they 
will always appear in absolutely the same directions. On the other 
hand, if the sun is the center and the earth revolves around it, they 
will appear in slightly different directions at different times of 
the year. 

In Fig. 17 let S represent the sun and A B the orbit of the earth. 
Suppose s is one of the fixed stars. When the earth is at A this star 
will be seen in the direction As; six months later when the earth is 
at B it will be seen in the direction Bs. Every star will be slightly 
displaced in this fashion because of the earth's motion around the 
sun. This difference in direction of a star, as seen at two different 
times of the year, is called its parallax. Consequently, in order to 
determine whether the earth is fixed or moves around the sun, it is 



ASTRONOMY 45 

only necessary to observe whether the directions of the stars are 
absolutely fixed or not. 

It is clear from the figure that the farther the star is away the 
smaller will be its change in direction as seen from the two points A 
and B. It is analogous to the fact that if one looks at an object near 
his face, first with one eye and then with the other, he will see it in 
somewhat different directions. If he looks at it with both eyes it will 
be necessary for him to turn them in slightly. As a matter of fact, 
one of the best ways he has of judging distance is by the amount he 
has to turn the eyes in to see the object. If he looks at a distant object 
his eyes are sensibly parallel. In Fig. 17, the points A and B corre- 
spond to the positions of the two eyes of the observer, and the star 
to the object observed. 




Fig. 17. The Difference in Direction of the Star S as Seen from the Earth at 
Two Different Times of the Year Proves the Revolution of the Earth 

The fact that the stars should have parallaxes if the earth 
revolved around the sun was known at a very early date. Tycho 
Brahe observed them in order to discover whether they were sen- 
sibly fixed in the sky or not. So far as his observations went they 
did not change their positions during the year. He inferred from this 
that the earth remained fixed and that the sun moved. His error 
was due to the fact that his observations were not sufficiently accurate 
to show the slight displacement which the stars have. His observa- 
tions were made shortly before the invention of the telescope and 
he could not measure the minute angles through which the stars were 
displaced. In fact, their distances are so great and the parallactic 
displacements are so small that the nineteenth century was well 
advanced before astronomers succeeded in finding any stars with 
measurable parallaxes. At the present time, in spite of the great 
precision of modern instruments, the parallaxes of only 50 or 60 
stars have been directly measured, but these 50 or 60 prove in the 
most rigorous fashion that the earth actually revolves around the sun. 



46 



ASTRONOMY 



Revolution of the Earth Proved by Aberration of Light. The 

earliest direct proof that the earth revolves around the sun was made 
in 1728 by the discovery of what is called the aberration of light. 



Fig. 18. The Apparent Direction of the Stars Is Slightly Changed by the Motion 
of the Earth across the Path of the Rays of Light from Them 



Suppose rain is falling vertically and one stands still in it. 
Then it appears to him that it is coming straight down. Suppose 
he walks rapidly through it; then it seems to meet him obliquely, 
striking him in the face. Suppose he rides through it rapidly; then 
it seems to meet him more obliquely. The angle at which it seems 
to strike him depends upon the speed with which it falls, and the 

speed with which he goes across the line of 
its motion. 

If one moves at right angles to the di- 
rection of the light rays a similar phenom- 
enon is observed. In Fig. 18, suppose AB 
is the direction of the earth's motion. Sup^ 
pose the continuous lines which meet it at 
right angles are the direction of the rays 
of light from a distant star. Because of 
the earth's motion along AB the rays of 
light from the star will appear to come in 
along the dotted lines. This causes the 
star to be apparently displaced in the di- 
rection in which the observer is going. It 
follows from the velocity of light and the 
velocity that the earth must have if it 
goes around the sun, that this displacement should be about 20 
seconds of arc. This is a quantity which is easily observable and 
does not depend upon the distance of the stars. The problem 




Fig. 19. A Star Apparently De- 
scribes Yearly a Small Curve in 
the Sky Because of the Ab- 
erration of Its Light 



ASTRONOMY 47 

is to determine by observations whether the star is thus displaced 
or not. 

In Fig. 19, let ABCD represent the orbit of the earth and s the 
actual position of a star. Suppose the earth's motion is in the direc- 
tion ABCD. When the earth is at A the star will be displaced 
by the aberration in the direction in which the earth moves and 
will be seen at a. Similarly, when the earth is at B, C, and D, 
the star will be seen at b, c, and d, respectively. That is, while the 
earth describes its orbit the star will describe an apparent small curve 
in the sky whose radius is about 20 seconds. This is the fact which 
was discovered in 1728 by the English astronomer James Bradley. 
The direction and the amount of the displacement agree precisely 
with the theory that the earth revolves around the sun, and con- 
stitute an absolute proof of its motion. 

Revolution of the Earth Proved by the Spectroscope. The spec- 
troscope is an instrument by means of which it is possible to deter- 




Fig. 20. When the Earth Is at A, It Is Approaching the Star S. When the 

Earth Is at &, It Is Receding from S. The Spectroscope Shows 

This Motion and Proves the Revolution 

mine whether the observer is approaching or receding from any 
luminous object. It enables him not only to determine whether he is 
approaching or receding, but also the relative speed. This is all that 
we need to know of the spectroscope at the present time. The 
discussion of the construction of this instrument and its uses will 
be treated in connection with the sun. 

If the earth is the center of the system and the stars are fixed, 
the spectroscope will show that we neither approach nor recede from 
them. On the other hand, if the sun is the center and the earth 
revolves around it, the spectroscope will show that at certain times 
of the year we are approaching the stars and that at other times we 
are receding from the same stars. In Fig. 20, let $ represent the sun 
and AB the earth's orbit. Suppose the direction of the earth's 



48 ASTRONOMY 

motion is indicated by the arrow. Let s represent the position of a 
distant fixed star. When the earth is at A it will be approaching the 
star and six months later when it is at B it will be receding from it 
at the same rate. 

In order to determine by this method whether the sun or the 
earth is the center it is necessary to make spectroscopic observations, 
of stars at the proper times. It is clear from the figure that it is 
most convenient to take stars in or near the plane of the earth's orbit. 
Now, the actual observations made on thousands of stars show us 
that when, according to the theory that the earth revolves around 
the sun, we should be approaching the stars we are actually approach- 
ing them, and that we recede when the theory demands that we 
should be receding. In this way the spectroscope proves with cer- 
tainty that the earth revolves around the sun. It not only gives us 
this fact but it determines for us the speed with which it goes. Since 
the length of the year is known and the speed is determined by means 
of the spectroscope, we can compute the whole circumference of the 
earth's orbit, and consequently the distance from the earth to the 
sun. This is only one of many methods of determining this distance, 
and it is significant that the result agrees very closely with that 
found by all the other methods. 

Shape of the Earth's Orbit. It was assumed in the first discus- 
sion of the subject that the orbit of the earth is circular. Obviously, 
this is the simplest closed curve. If the orbit is a circle with the sun 
at its center, then the sun will be at the same distance from the earth 
throughout the year and consequently will be always of the same 
apparent size. It is clear that an object looks smaller the farther 
one is away from it, but if the orbit of the earth is not a circle then 
its distance from the center will vary during the year and the apparent 
size of the sun will change correspondingly. 

It is found from the actual observations of the apparent diameter 
of the sun that it changes throughout the year. At one time it is 
nearly two per cent greater than it is six months from that time. 

The shape of the earth's orbit and the way in which the earth 
moves in it can be determined rather easily from the observations. 
Suppose, in Fig. 21, S represents the sun and the curve E i E 2 E 3 E i 
the orbit of the earth (the elongation is greatly exaggerated). Sup- 
pose an observation is made when the sun is in the direction EiS. 



ASTRONOMY 49 

A convenient scale can be chosen and the line E X S laid down. Sup- 
pose at a later date the sun is seen in the direction E 2 S. The line 
can be laid down and the distance E 2 S determined by the apparent 
size of the sun. If the apparent diameter of the sun is smaller when 
observed at E 2 than at E lf then E 2 is farther from S than is E v If 
the diameter is one per cent smaller, then the distance is one per cent 
greater, and similarly for any other differences. In this fashion the 
point E 2 is located. In a similar way the positions of the lines 
E 3 S and E 4 S and the distances are determined, and the points 
which represent the position of the earth are laid down. The curve 
drawn through them will represent the orbit of the earth in shape, 
the position of the sun in its interior, and the way in which the 
earth moves in its orbit. Such observations as these have shown 
that the orbit of the earth is an 
ellipse, and that the sun is at one 
of its foci. See Fig. 5. 

It is also found that the earth 
moves in its orbit so that the 
line from the sun to it sweeps 
over equal areas in equal inter- 
vals of time. For example, if the 

r Fig. 21. The Line Joining the Earth and 

time required for the earth tO the Sun Sweeps Over Equal Areas in 

^ Equal Intervals of Time 

move. from E x to E 2 is the same 

as that required for it to move from E 3 to E 4 , then the area E X SE 2 

is equal to the area EzSE^. 

Obliquity of the Ecliptic. The sun, moon, and stars as seen 
from the earth appear to be on a great sphere enclosing them all, 
which is called the celestial sphere. Since they are at very different 
distances from us they are not actually on any sphere, but only seem 
to be on one. In describing their directions from us it is permissible 
to regard them as being on this celestial sphere. The apparent path 
of the sun in its apparent yearly motion around the earth is a 
great circle on the celestial sphere which is called the ecliptic. It is 
not the path of the sun but the projection of its apparent path on 
the celestial sphere; or, it may be defined as the circle in which the 
plane of the earth's orbit cuts the celestial sphere. 

The plane of the earth's equator cuts the celestial sphere in 
another great circle known as the celestial equator. The angle between 




50 ASTRONOMY 

the celestial equator and the ecliptic is called the obliquity of the 
ecliptic. 

In Fig. 22, the line from the sun to P is parallel to the earth's 
axis. The circle CABV represents the celestial equator, which is 
parallel to the earth's equator, and the circle SAWV represents the 
ecliptic, which is in the plane of the earth's orbit.- As seen from' 
the earth the sun moves along the ecliptic from west to east, indi- 
cated in the figure by the arrow. The place where the sun crosses 
the equator from south to north, indicated by V in the figure, is 
called the vernal equinox, and the place where it crosses from north 

^ ^^p to south, indicated by A in the 

y< /N* figure, the autumnal equinox. 

/ I \ The earth is at a when the sun 

Br" ~~~-^ AA J \ seems to be at the point A. And 

/ V'~~~. %jj^ ^ "~~"^ \ similarly the earth is at w, v, s 

w\ ^xff^ vW/S* Jlt v x z 5 wnen the sun appears to be at 

\ \^ \T &~~ i Jk\ ty, F, S. The axis of the earth 

\ ^^^S^^? ]c is perpendicular to the plane of 

\ / the equator and keeps always par- 

n. y allel to its initial direction while 

^ ~>^^ the earth moves around the sun. 

Fig. 22. The Relations of the Earth and the „„:„„ „f +u~ C^,-.: „~„ 

Plane of its Orbit to the Ecliptic and Precession of the hquinoxes. 

the Celestial Equator rr , 1 ,. . . , . , . 

I he ecliptic is a curve which is 
almost absolutely fixed in the sky. The only changes in it are due 
to the slight irregularities in the motion of the earth produced by 
the attractions of the other planets. On the other hand, the celestial 
equator is not fixed because the plane of the earth's equator is 
changed rather rapidly by the attraction of the sun and moon on 
the equatorial bulge of the earth. The angle between the plane of 
the earth's equator and the plane of the ecliptic, or the obliquity of 
the ecliptic, remains fixed; but the position of the plane shifts so 
that the points A and V go westward on the ecliptic to A and V x . 
Since A moves in the direction opposite to that of the apparent 
motion of the sun the change is called "precession." The rate is about 
50.2 seconds of arc annually, from which it follows that the equinoxes 
will make a complete revolution only after 25,800 years have elapsed. 
In spite of the fact that the precession is very slow, it was discovered 
by the ancient Greeks three centuries before the beginning of the 



ASTRONOMY 



51 



Christian Era. This is an evidence of the perfection which astro- 
nomical science had attained among them. 

As we shall see, the seasons depend upon the obliquity of the 
ecliptic. If we should define as the year for ordinary purposes the 
time it takes the sun to go from any apparent point on the ecliptic 
back to the same point again, we should find as the consequence of 
the precession of the equinoxes that the sun is not at the vernal 
equinox at the same time on succeeding years. For example, if 
some time it is found that the sun is at the vernal equinox precisely 
at the beginning of the year it will pass the vernal equinox again 




The Altitude of the Pole of the Sky Equals the 
Latitude of the Observer 



slightly before the end of the year. Consequently, with this sort of 
year we should have continually shifting seasons. Therefore, the 
year which is adopted for ordinary civil purposes is the time it takes 
the sun to go from the vernal equinox V around to the vernal 
equinox V 1} Fig. 22, which is little less than a complete revolution. 
Using this year, the seasons always remain fixed with respect to it. 
Causes of the Seasons. The direct cause of the seasons is the 
varying amount of light and heat received from the sun per day. 
It is a matter of common observation that in the summer time the 
sun shines more hours per day than in the winter time and that at 
midday its rays fall more nearly perpendicularly. The problem 
before us is to discover the laws of these changes on the basis of 



52 ASTRONOMY 

the motions of the earth, and to apply them to a determination of 
the extent of the changes. As a preliminary to this discussion it 
will be necessary to determine the relation between the latitude of 
the observer and the altitude of the pole in the sky, as he sees it, 
and that of the equator where it crosses his meridian. In Fig. 23, 
let the circle E represent the earth and PP' its axis of rotation.* 
Suppose the observer is at 0; then his latitude is /. The posi- 
tion of the pole in the sky is that point on the celestial sphere 
towards which the line P'P points. The celestial sphere is so 
remote that a line from towards the pole will be parallel 
to P'P. The equator will be at right angles to P'P. The hor- 
izon of the observer at is indicated in the figure. The angle 
between the plane of the horizon and the line from the observer to 
the pole is at a, and from the observer to the equator is b. The 
sides of the angle a are, respectively, perpendicular to the sides of the 
angle /, and it follows therefore from plane geometry that a=l. 
That is, the distance of the north pole of the sky above the north 
point of the horizon in degrees is always equal to the latitude of the 
observer. It can be seen from the figure that the angle b= (90° — /). 
That is, the latitude of the equator on the meridian above the south 
point of the horizon in degrees is equal to 90 degrees minus the lati- 
tude of the observer. 

As an example of these results it may be noticed that if an 
observer is on the earth's equator where his latitude is zero, the 
north pole of the sky is at the north point of the horizon; and the 
point where the equator cuts the meridian is directly over his head. 
On the other hand, if he were at the earth's pole so that his latitude 
were 90°, the celestial pole would be directly over his head while the 
equator would be on the horizon. 

In Fig. 24, represents the position of the observer and N, E, S, 
and W the north, east, south, and west points of his horizon. The 
latitude of the observer is such that the north pole of the sky is ac 
P and the equator at AWE E. Now, because of the rotation of 
the earth, the sun has an apparent diurnal motion from east to west, 
completing a circuit of the sky in one day. Suppose the sun is at 
the vernal equinox, the point V in Fig. 22. Then it is on the celestial 
equator and it is clear that the diurnal motion is along the circle 
E A WE in the direction indicated by the arrow. This is a great 



ASTRONOMY 



53 




circle and is bisected by the horizon. Consequently, when the sun is 
on the celestial equator it is half of the twenty-four hours above the 
horizon, and the remaining half below it. 

Besides this diurnal motion the sun has a slow motion along 
the ecliptic. After it passes the point V in Fig. 22, it is north 
of the equator, and it reaches its greatest distance north at S, when 
it is 23.5 degrees north of the equator. Now consider Fig. 24, 
which shows the circles of the 
diurnal motion. When the sun is 
23.5 degrees north of the equator 
it moves on the circle BKIF. It 
is above the horizon while it 
moves over the arc FBK, and 
below it while it moves over the 
arc KIF. It is clear from the 
figure that it is above the horizon 
considerably more than one-half 
of the 24 hours. Six months from 
this time the sun will have moved 
around to the point W of Fig. 22, 
when it will be 23.5 degrees south 

of the equator. At this time its diurnal motion is along the circle 
DCLG. It is above the horizon while it describes the arc DCL, 
and below it while it describes LGD. It is clear from the figure 
that in this case the sun is above the horizon much less than one-half 
of the 24 hours. 

To summarize the matter, we may state that the sun is above 
the horizon one-half of the 24 hours when it is on the celestial equa- 
tor, whatever the latitude of the observer may be. It is on the celes- 
tial equator twice a year at the vernal and autumnal equinoxes. 
When it is north of the equator, moving from the vernal to the au- 
tumnal equinox, it is above the horizon more than one-half of each 
24 hours. (These statements should, of course, be reversed if they 
are to be made for observers in the southern hemisphere.) In the six 
months while it is south of the equator, viz, while it is moving from 
the autumnal equinox to the vernal equinox, it is above the horizon 
less than one-half of each 24 hours. This variation in the length of sun- 
light per day is one of two chief causes in the changes in the seasons. 



Fig. 24. The Diurnal Circles of the Sun at 

Different Distances from the 

Celestial Equator 




54 ASTRONOMY 

The second important reason why the seasons change is that the 
direction of the sun's rays at noon, for instance, varies throughout 
the year. In Fig. 24 the horizon SENW is given and it is seen that 
the sun's rays strike the surface of the earth at the angle AOS when 
the sun is on the equator. When it is north of the equator they 
strike nearer to the perpendicular at the angle BOS; and when it* is 
south of the equator they strike more obliquely at the angle COS. 
It is easy to show that the nearer the perpendicular the sun's 
rays strike the more they heat the surface. In Fig. 25, AB represents 

the cross-section of a certain 
beam of light. If the rays 
should strike the surface per- 
pendicularly they would all fall 
"*" on an area whose distance 

Fig. 25. When the Sun's Ravs Strike the Earth i i i_ t rt t> ±. -a 

Obliquely They Are Spread Out over a Large aCrOSS WOUld be AB. £>Ut II 
Area and Their Heating Effect Is Small , , , , ., , „ 

they should strike the surface 
obliquely, as is indicated in the figure, then the same rays would be 
spread over the larger area a B. Consequently, being spread over a 
larger area, they would illuminate and heat it less than when spread 
over the smaller area. Therefore, when the sun is high in the sky 
at noon it heats the surface more than it does when its rays fall 
obliquely. This matter is illustrated by the fact that the temperature 
is higher at noon, when the sun's rays fall almost perpendicularly, 
than it is when the sun is rising or setting. 

Relative Amounts of Sunlight in Different Latitudes. It is 
often supposed that the equatorial part of the earth is that which 
is not only hottest, but which receives the most hours of sunlight. It 
is clear from the discussion above that the northern hemisphere 
receives more light than the average in the summer and less in the 
winter, and it is at least conceivable that these two extremes exactly 
balance. A mathematical discussion shows that they do exactly 
balance for all latitudes. 

In order to illustrate the matter let us take the two extreme 
cases, viz, where the observer is at the earth's equator and where 
he is at its pole. Fig. 26 represents the positions of the diurnal circles 
relative to the horizon when the observer is at the earth's equator. 
When the sun is on the celestial equator it rises at E and travels 
along the diurnal circle EAWH, during which time it is above the 



ASTRONOMY 



55 



horizon. It is seen from the figure that this is exactly one-half of its 
whole diurnal circle. Similarly, whether it is north of the equator 
and moving along the diurnal circle FBKI, or south of the equator 
and moving along the diurnal circle DCLG, it is also exactly one- 
half of each 24 hours above the horizon. Therefore, at the earth's 
equator the sun shines exactly one-half of the time. 

But when the observer is at the earth's pole, the celestial pole 
is directly over his head, Fig. 27, and the equator coincides with 
his horizon. Consequently, the sun shines only when it is north of 
the equator, which is one-half of the year. Therefore, in this case 
also the sun shines one-half of the whole year. 

While the total number of hours of sunlight per year are the 
same at the equator and at the pole, as has just been shown, and 



c^-~ 


X 






'° i 


M 




£ ; 


r 



-Jft 




Fig. 26. Diurnal Circles for an Observer 
at the Earth's Equator 



Fig. 27. 



Diurnal Circles for an Observer 
at the Earth's Pole 



also in all other latitudes as can be shown by proper mathematical 
discussion, it is to be remarked that their distribution is very differ- 
ent. At the earth's equator the sun shines an equal number of hours 
during each day throughout the year. At the pole the sunshine is 
continuous for six months. It follows from this that the variation in 
the seasons is much greater at the pole than it is at the equator. If 
one were to take into account the refraction of light, which elevates 
the sun a distance about equal to its diameter when it is on the hori- 
zon, it would be found that the total number of hours during which 
the sun is visible from the pole is greater than that during which it is 
visible from the equator. 



56 ASTRONOMY 

While the number of hours of sunshine in a year is the same for 
all points on the earth it must not be supposed that the total amount 
of sunlight received is the same for all points. On the earth's equator 
twice each year the sun passes through the zenith and every day 
passes near to it. There is, therefore, a time each day when its 
rays strike nearly perpendicularly on the surface. On the other 
hand, at the pole the sun never gets more than 23.5 degrees above 
the horizon and its rays always strike very obliquely. Consequently, 
the amount of light and heat received at the equator are very much 
greater than at the pole. The amount received at the equator in a 
year is about the same as it would be if the sun stood still 17 degrees 
above the horizon, for the whole year. The amount received at the 
pole for the whole year is about the same as it would be if the sun 
stood still at an angle of 5.8 degrees above the horizon. It follows 
from this that at the equator the amount of light and heat received 
are a little more than three times that received at the pole. 

If it were not for the obliquity of the ecliptic, the pole would 
receive infinitely little sunlight because — except for the refraction — 
the sun would always be exactly on the horizon. Thus, it follows 
that the obliquity of the ecliptic causes a higher mean temperature 
at the pole than it would otherwise have. At the equator, on the 
other hand, the sun passes through the zenith but twice in the year. 
Consequently, the equator receives less sunlight and heat than it 
would if the obliquity of the ecliptic were zero. Hence, a conse- 
quence of the obliquity of the ecliptic is that the equatorial regions 
are cooler and the polar regions warmer than they would otherwise 
be; that is, the obliquity of the ecliptic has a tendency to equalize 
the earth's climate, taken as a whole. 

An interesting fact in this connection is that, theoretically, 
the highest temperatures would not be found exactly at the equator. 
When the sun is on the equator it passes through the observer's 
zenith. This happens, however, on but one day, for it rapidly passes 
away from the equator. This is made clear in Fig. 22, since the sun 
is on the earth's equator when it is at V, which it quickly crosses. 
On the other hand, when the sun is near S, Fig. 22, its distance north 
of the equator changes very slowly. For some weeks it does not vary 
enough to make any material difference. For an observer who is 
just far enough north of the equator so that it then passes through 



ASTRONOMY 57 

his zenith, it will be above his horizon more than one-half of each 24 
hours, and will pass very near his zenith each day. At this time he 
is receiving more light and heat than is ever received in a similar 
length of time by an observer at the earth's equator. It follows from 
this that theoretically the temperature should be highest near the 
points which are approximately 23.5 degrees north and south of 
the earth's equator. 

Lag of the Seasons. From the astronomical point of view 
the times when the sun is at V and A, Fig. 22, are corresponding 
seasons. It is found from the observations that the sun is at the 
vernal equinox on March 21 and at the autumnal equinox on Sep- 
tember 23. (The dates on which it passes the equinoxes can vary a 
day or so from those just given because of the shifting leap year.) 
It is perfectly clear from the point of view of the climate that March 
21 and September 23 are not corresponding times in the year. The 
reason is the seasons lag, as we say. There is a corresponding lag 
in the day which, being simpler, will be first discussed. 

From the standpoint of the amount of light and heat received, 
nine o'clock in the morning and three o'clock in the afternoon are 
corresponding times of day. But almost invariably the temperature 
is higher at three o'clock than it is at nine o'clock. The reason is 
that at nine o'clock the earth is receiving more heat than it radiates. 
This continues until noon when the maximum amount is received. 
But at this time it is also receiving more than it radiates and con- 
tinues to do so until the increase of its temperature and the decrease 
in the amount received cause the radiation to equal exactly that 
which is received. After that the temperature begins to fall. But 
under normal weather conditions this occurs considerably after noon. 
The time after noon at which the highest temperature is reached is 
called the lag of the noon. There is a corresponding lag in the time 
of lowest temperature at night. Of course, when the sun has set no 
light and heat are received from it directly until morning, but it is 
farthest below the horizon at midnight. Instead of this being the 
time of the lowest temperature, as a rule the temperature steadily 
falls from sundown until almost sunrise in the morning. 

Now consider the seasons. As the sun mounts higher and higher 
in the sky in the spring so that more and more heat is received daily, 
the earth gets considerably warmer both because of the greater 



58 ASTRONOMY 

number of hours of sunshine and also because of the high altitude 
of the sun at noon. During the spring months, for example, April 
and May, the earth receives more heat in the northern hemisphere 
than is lost by radiation, and the temperature rises. This continues 
until about the 21st of June when the sun arrives at the point S, 
Fig. 22, which is its greatest distance north of the equator. But at 
this time the maximum amount of heat is received and this is more 
than that which is radiated. Consequently, the mean temperature 
continues to rise for some time after the 21st of June. It becomes 
stationary only when the temperature rises to such a point that the 
increased radiation and the decreased amount received exactly 
balance. In moderate latitudes this lag amounts to some weeks. 

If the earth had no atmosphere and if it radiated the heat as 
fast as it was received there would be no lag of the seasons. Atmos- 
phere, is one of the causes of the lag of 
the seasons. The more it absorbs light 
and heat as they come to the earth, and 
prevents their escaping as the earth 
radiates them out, the more the seasons 
will lag. It is a matter of common ob- 
1 %^J££SS%S&E* U scrvation that there is a greater lag to 
Be SfThelart\?Orbit icity the seasons in low altitudes, especially 
where the atmosphere is moist, than there 
is on the high and dry plateaus. 

Effect of the Eccentricity of the Earth's Orbit upon the Seasons. 
In the discussion up to this point it has been assumed tacitly that 
the orbit of the earth around the sun is a circle. x\s explained above, 
it is an ellipse and the earth is about three per cent nearer at the 
point nearest the sun than it is when most remote. Consequently, 
the amount of light and heat received depends to some extent upon 
the varying distance of the earth from the sun. It should be said, 
however, that this is not so important a cause as that discussed above. 
There is a very, interesting indirect result of the eccentricity 
of the earth's orbit, viz, that the seasons in the northern and southern 
hemispheres are not of equal length. In Fig. 28, V represents the 
position of the earth when the sun is at the vernal equinox, and A 
its position when the sun is at the autumnal equinox. The point P 
is the earth's position when it is nearest the sun. It is almost midway 




ASTRONOMY 59 

between A and V, but a little nearer V than A. It follows from the 
law of areas that the earth will pass from A through P to V in a 
shorter time than is required for it to pass from V through Q to A. 
If we count the days from March 21 to September 23 it is found that 
the summer, from the astronomical point of view, in the northern 
hemisphere is 186 days and the winter, viz, the time from September 
23 to March 21, is 179 days. The more exact figures are: the length 
of the summer in the northern hemisphere is 186| days, and the 
winter 179 days. That is, because of the eccentricity of the earth's 
orbit, the summer is 1\ days longer than the winter. In the southern 
hemisphere the conditions are reversed. 

One might suppose from this that there were peculiar climatic 
advantages in the northern hemisphere. The facts are, however, 
that the same amount of light and heat are received in the year at 
any point in the northern hemisphere as are received at any point 
having an equal latitude in the southern hemisphere. The increase 
in the length of the summer in the northern hemisphere is exactly 
offset by the greater distance from the sun during this time, and its 
nearness to the sun in the winter in the northern hemisphere is 
exactly compensated by the fact that the winter is shorter. The 
more exact statement is that equal latitudes in the northern and 
southern hemispheres receive exactly the same amount of light and 
heat in corresponding parts of any seasons. The chief difference is 
that in the northern hemisphere the tendency is for the climate to be 
somewhat more uniform, since, when the rays strike nearest to the 
perpendicular, the earth is farthest from the sun. The conditions 
are reversed in the southern hemisphere. The fact, however, that 
there is so much more water in the southern hemisphere than there 
is in the northern, probably more than counterbalances these astro- 
nomical causes for an equable climate in the northern hemisphere. 

The eccentricity of the earth's orbit slowly changes and the 
direction of its major axis PQ also chan es because of the attrac- 
tions of the other planets for it. Likewise it was seen above that 
there is a precession of the equinoxes, so that the line .IT does not 
remain fixed. It follows from this that not only does the elongation 
of the orbit of the earth change, but also the positions of the lines 
PQ and AV change relative to each other. In about 10.0(H) years 
from now the conditions will be the opposite of those wo have at 



60 ASTRONOMY 

present. At that time the summers in the northern hemisphere 
will be shorter than the winters and more heat will be received per 
day than during the summers in the southern hemisphere. In the 
course of a very long time, counted by tens of thousands of years, 
the eccentricity of the earth's orbit will be greater than it is at present, 
though now it is decreasing and will decrease very slowly for a long 
time. 

It has been supposed that an unequal distribution of the light 
and heat received from the sun throughout the year are favorable to 
glaciation. An English geologist, Croll, suggested, as an explanation 
of the ice ages which the earth has experienced, that they were 
due to the fact that at certain times the northern hemisphere had 
long, cold winters and short, hot summers. He supposed that the 
accumulation of ice and snow in the winter time, under those circum- 
stances, would be so great that they would not be melted in the 
summer. This theory has been abandoned because, according to 
it, the intervals between the ice ages would be counted by hundreds 
of thousands of years, whereas geologists find they were much closer 
together than this. Likewise there have been ice ages very probably 
at the same time in both the northern and southern hemispheres. 
According to this theory, when the conditions are favorable to 
glaciation in one hemisphere they are unfavorable to it in another, 
and glaciation should not be simultaneous both north and south of 
the equator. 




STAR CLUSTER AND NEBULA IN CYGNUS 
Takcii with a 10-inch Bruce lens. The streak at the top of the picture was made by a large meteor 



ASTRONOMY 

PART II 



THE CONSTELLATIONS 

Problem of Locating the Constellations. The most careless 
observer of the sky has noticed that the stars are not uniformly 
spread over it. Almost everyone is familiar with the Big Dipper 
and the Pleiades, otherwise known as the Little Dipper. These 
natural groups of stars were given names in antiquity by early 
observers and are called constellations. Their names often strike us 
as being most fantastic and far-fetched. Many of them are the 
names of wild animals. For example, we have the Great Bear, 
the Lesser Bear, the Lion, the Eagle, the Leopard, etc. 

If the sky is watched for a few hours it is observed that these 
groups of stars move across it from the east toward the w T est. The 
fact that they are not fixed in the sky leads to some little difficulty 
in describing their positions. Suppose an observer watches them a 
few nights until he finds how they move throughout the night and 
knows where they appear at any time of the night. If he then ceases 
to observe them for a few months and again returns to his observa- 
tions, he will find things are quite different. Those stars which at 
his first observations were visible high in the sky late in the night 
are a few months later visible early in the evening. Thus, he finds 
that not only do the stars change their positions in the sky during 
the night but that on successive nights these positions are not 
the same. There is a continual shift throughout the year. 

It follows from these changing positions of the stars and the 
necessity in certain astronomical work of locating them with the 
very highest degree of precision, that it is necessary to adopt some 
machinery for describing their positions. As was stated above, all 
the heavenly bodies seem to be seen on a great sphere. This sphere, 



62 



ASTRONOMY 



surrounding the visible universe and having the earth as its center, 
is called in astronomy the celestial sphere. The problem of the 
astronomer is to locate the positions of the heavenly bodies on this 
sphere, which is in many respects similar to the problem of locating 
the position of a place on the earth, which for ordinary geographic 
purposes may be regarded as a sphere. From the standpoint of* 
geometry the two problems are exactly the same. They appear to 
us to be slightly different because in the case of the earth we are on 
the outside and in case of the celestial sphere we are on the inside. 
But in representing the celestial sphere by a globe we are on the 
outside, and this is sometimes a little confusing. However, by a 

little use of the imagination the 
identity of the two problems can 
be seen, and our knowledge of 
what is done in geography will 
assist in understanding how the 
corresponding problem is solved in 
astronomy. 

Geographical System. The lines 
on the earth by means of which 
we locate places fall into two fun- 
damentally distinct systems: (1) 
there are the equator and the 
system of small circles parallel to 
it; (2) there are the great circles 
which pass through the poles of the earth and cut the equator at 
right angles. The circles to be defined are the equator (after which 
all the parallel circles are given) and the particular great circle per- 
pendicular to the equator from which we count. 

In locating the position of a place on the earth, we give its 
distance north or south of the equator, called its latitude, and its 
distance east or west of some selected meridian, called its longitude. 
The meridian is selected for its convenience, the ones in most 
common use being those through the Royal Observatory at Green- 
wich, England, the one through the Naval Observatory at Washing- 
ton, and those in other countries passing through their national 
observatories. The position of Chicago, for example, is about 41° 50' 
north of the equator and 78° 22' west of the meridian of Greenwich. 




Fig. 29. The Latitude and Longitude 
Circles on the Earth 



ASTRONOMY 



63 



In Fig. 29, EAB represents the equator and PP' the poles. 
Suppose the meridian PAP' is the fundamental meridian from which 
longitudes are counted. Consider a point at C. The latitude is the 
arc BC, and the longitude is the arc AB measured along the equator. 
It is to be noted that it must be measured along the equator 
because the latitude circle through C is a small circle. 

Horizon System. In defining the circles of this system it is 
simpler to start with the zenith than with the horizon. The zenith is 
the point overhead where the plumb-line extended upward pierces 
the celestial sphere. The nadir is the point below 180° from the 
zenith. The horizon is the great circle of the celestial sphere 90° 
from the zenith and nadir. This is the astronomical horizon and it 
may differ in particular instances considerably from the sensible 
horizon which is determined by 
the apparent union of earth and 
sky, and depends, obviously, 
upon all sorts of irregularities. 
The horizon corresponds to the 
equator in the Geographical Sys- 
tem. The small circles parallel 
to the horizon, corresponding to 
the circles of latitude in the 
Geographical System, are called 
parallels of altitude. 

The circles corresponding to 
the meridians in the Geograph- Fig ' 30 - The Horizon System of Circles 
ical System are the circles on the celestial sphere which pass through 
the zenith and nadir and cut the horizon perpendicularly. They 
are called vertical circles because they cut the horizon vertically. 

The position of a point on the celestial sphere is determined by 
giving its distance above or below the horizon and its distance corre- 
sponding to longitude. The distance from the horizon is called the 
altitude, plus if above and minus if below. 

The vertical circle from which the other distances are counted 
is the one passing through the zenith and the south point. This 
second distance, which is called azimuth, is counted westward from 
the south point around to the foot of the vertical circle through the 
object in question. Thus, in Fig. 30, suppose C is a celestial object 




64 ASTRONOMY 

whose altitude and azimuth we wish to give. Its distance above 
the horizon measured along the vertical circle is BC, which is its 
altitude. Its azimuth is the arc starting from S measured westward 
through W and N to B, which, in the present example, is somewhat 
greater than 180°. In this respect the scheme differs a little from 
the Geographical System, where longitudes are counted both east- 
ward and westward, and azimuth only westward. There is nothing 
fundamental in this method, but it is found simpler to count it all the 
way around to 360 degrees, rather than to be under the necessity of 
always stating whether it is counted eastward or westward. 

The reason that azimuth is counted westward instead of east- 
ward is that the stars in their diurnal motions go from east to west 
across the sky. Counting the azimuth westward, we find that it 
increases as the night goes on. When a star is on the meridian its 
azimuth is zero and as it passes west of the meridian its azimuth 
steadily increases. If the azimuth were counted in the other direction 
from the south point, then the azimuth of a star, as it crosses the 
meridian, would pass from zero to 359 degrees, and then continually 
decrease. The inconvenience of such a method as this is at once 
evident. 

Equator System. In defining the Equator System it is simplest 
to start with the celestial pole. In this work reference will be contin- 
ually made to the north pole, since we live in the northern hemisphere 
of the earth, but corresponding statements can in every case be made 
for the southern pole. The celestial pole is the center of the diurnal 
circles which the stars describe (see Fig. 11); or it is the place 
where the earth's axis extended northward pierces the celestial sphere. 

In Fig. 31, let be the position of the earth and P and P' the 
positions of the celestial poles. The celestial equator is the great 
circle on the celestial sphere 90 degrees from the celestial pole, or 
it is the great circle in which the plane of the earth's equator cuts 
the celestial sphere. The small circles parallel to the celestial equator 
are called parallels of declination. In Fig. 31 VEB represents the 
equator and DCF a parallel of declination. 

The celestial equator corresponds to the earth's equator in the 
Geographical System, and the parallels of declination correspond pre- 
cisely to the parallels of latitude. In fact, these circles on the celestial 
sphere are parallel to the corresponding ones on the earth. 



ASTRONOMY 65 

The circles which correspond to the meridians on the earth pass 
through P and P' ', Fig. 31, and are perpendicular to the equator. 
They are called hour circles for reasons which will be explained 
presently. The fundamental hour circle from which distances are 
counted is the one which passes through the vernal equinox, repre- 
sented by V in Fig. 31. 

The distance north or south of the equator, corresponding to 
latitude on the earth, is declination; positive if north, negative if 
south. The distance corresponding to longitude on the earth is 
right ascension, which is counted eastward from the vernal equinox 
along the equator to the foot of the hour circle through the object. 
This differs from longitude on 
the earth in that it is counted 
only in one direction. 

If one wishes to give the 
position of C, Fig. 31, in the 
Equator System, he gives its 
declination, which is the arc BC, 
and its right ascension, which is 
the arc VB, measured eastward 
from V through E to B. 

Since the earth rotates on its 
axis from west to east, the sky 
apparently rotates from east to west. The point V is not a fixed 
point on the apparent sky, as one looks at it. It rises in the east at 
E daily, goes across the sky to the west and sets at W, passing around 
to E again. The star at C passes along the declination circle through 
D around to F and back to C daily. Its highest altitude is when it 
is on the meridian at D. It was shown above that the altitude of 
the equator on the meridian is 90 degrees minus the latitude of the 
observer. Consequently, the highest altitude of a star is 90 degrees 
minus the latitude of the observer plus the declination of the star. 
For example, if an observer is 40 degrees north of the equator and 
he observes a star whose declination is twenty degrees north, he finds 
that when it crosses its meridian its altitude is 90°— 40°+ 20° =70°. 

Its lowest altitude is when it is at F; on the point where the 
equator cuts the antimeridian NP', it is 90 degrees minus the lati- 
tude of the observer below the horizon. The lowest altitude of a 




The Equator System of Co- 
ordinates 



66 ASTRONOMY 

star in its diurnal motion is therefore 90 degrees minus the latitude 
of the observer, plus the declination of the star. For example, in 
the problem given above the lowest altitude of the star is — 90°+ 
40°+20°= —30°, or 30 degrees below the horizon. In this way it is 
found that, for an observer in latitude 40 degrees, the highest altitude 
of the sun, when it is at the summer solstice 23.5 degrees north of the 
equator, is 73.5 degrees, and its lowest altitude below the horizon is 
26.5 degrees. In the winter time, when the declination of the sun is 
23.5 degrees south, it is found in a similar way that its highest altitude 
in the day for an observer in latitude 40 degrees north is 26.5 degrees 
and its lowest altitude is —73.5 degrees. 

The reason that the circles passing through P perpendicular to 
the equator are called hour circles is that they move from east to 
west across the sky in their diurnal motions, making a circuit in 24 
hours. Consequently, if they are drawn one hour apart they will 
cross the meridian one after another at intervals of an hour. For 
this reason it is customary to count right ascension in hours rather 
than in degrees, though the relation is simple. The 360 degrees 
around the celestial equator are divided into 24 hours, from which it 
follows that one hour is equal to 15 degrees. 

It is readily seen from this how easy the problem of determining 
the right ascension of the stars is if one has a clock and a telescope 
mounted in the plane of the meridian. Suppose he keeps the tele- 
scope fixed and makes a record of the time the stars pass across its 
field, which is the time they pass the meridian. Suppose his clock 
is set so that it registers zero hours when the vernal equinox passes 
the meridian, and that it is marked to run from zero to 24. Then 
if a star passes at one o'clock its right ascension is one hour, and 
similarly for any other time. This is, in fact, the way the right 
ascensions of the stars are' determined. At the same time their 
declination can also be determined. If it is found how high they 
are above the horizon when they pass the meridian, their declination 
is at once given because their declination is equal to their altitude 
minus the altitude of the equator. If they are north of the equator, 
and consequently have an altitude greater than the equator, this 
comes out a positive result. On the other hand, if they are south 
of the equator their declination comes out negative. These results 
agree with the definitions of positive and negative declination given 



ASTRONOMY 



67 



above. Since the altitude of the equator is 90 degrees minus the 
latitude of the observer, it follows that the declination of the star 
is its observed altitude plus the latitude of the observer minus 90 
degrees. 

Ecliptic System. The ecliptic has been defined as the apparent 
path of the sun around the celestial sphere. It is a great circle cutting 
the celestial equator at the vernal and autumnal equinoxes and 
inclined to it by an angle of 23.5 degrees. In Fig. 32, KEMW 
represents the celestial equator and LVJA the ecliptic, which 
cuts the equator in V and A. As before, SWNE represents the 
plane of the horizon. 

The parallels to the ecliptic, 
which are not given in the dia- 
gram, are called the parallels of 
latitude. The distance north or 
south of the ecliptic is called the 
latitude. The great circles perpen- 
dicular to the ecliptic are called 
celestial meridians. The funda- 
mental one from which distances 
along the ecliptic are counted is 
the one passing through the vernal 
equinox. It follows that the fun- 
damental hour circle and the fundamental celestial meridian intersect 
at the vernal equinox. They do not, of course, coincide because the 
former is perpendicular to the celestial equator and the latter to the 
ecliptic. The distance from this fundamental celestial meridian 
counted eastward along the ecliptic to the foot of the celestial meridian 
through the object is called the celestial longitude. It is counted east- 
ward until the object is reached even up to 360 degrees. Since the 
vernal equinox goes around the sky in the diurnal motions of the 
heavens, as has been explained above, the Ecliptic System revolves in a 
similar fashion, but in this case the motion with respect to the horizon 
is considerably more complex than in the case of the Equator System. 
For one-half of the 360 degrees the ecliptic is above the equator, and 
for the other one-half it is below it. Consequently, during one-half 
of 24 hours the ecliptic cuts the meridian at a greater altitude than 
the equator, and during the other half at a lesser altitude. The 




Fig. 32. 



The Relation of HorizQn, Ecliptic, 
and Equator 



68 ASTRONOMY 

ecliptic cuts the meridian in 24 hours at all the altitudes at which 
the sun crosses the meridian in a whole year. The reason for this is, 
of course, that the sun passes around the ecliptic once in a year. 

Comparison of Systems. If one person were to describe to 
another verbally where certain stars could be seen it would evidently 
be the simplest for him to give their altitude and azimuth. Ha 
would immediately look into the sky and locate the objects. But 
if he were to write to a person in another place serious difficulties 
would arise. In the first place, the one who was to observe the 
celestial objects would see them at a different time. In general it 
would be both at a different time of the day and a different time of 
the year. Consequently, the description would fail unless additional 
data were given, because, as was stated in the beginning of the dis- 
cussion of the Horizon System, the altitude and the azimuth of the 
stars not only change during the night but for a given time of night 
change through the year. 

There is another reason why the Horizon System would not 
be simple unless the observer were to look at the place where the 
person was who gave him the description. This second reason is 
that the position of an observer's horizon depends upon his location 
on the earth. This follows obviously from the fact that the zenith, 
and therefore indirectly the horizon, depends upon the direction of 
the plumb line of the observer. Altogether, therefore, in order to use 
the Horizon System as a means of describing the location of celestial 
objects it is necessary not only to give their altitude and azimuth 
but also the time of day, the day of the year, and the position of 
the observer. Obviously, for catalogue purposes, this system is 
inconvenient. In a word, this system of reference points and lines 
slides on a celestial sphere. 

The Equator System is distinguished by the fact that its refer- 
ence points and lines are fixed among the stars. The position of the 
celestial pole and the celestial equator are altogether independent of 
the observer's position. Likewise the vernal equinox, from which the 
right ascensions are counted, is independent of the observer's posi- 
tion, the time of the day, or the time of the year. A slight correc- 
tion to this statement is necessary because of the precession of the 
equinoxes as explained above. This is a very slow process and need 
not be considered in the present connection. 



ASTRONOMY 69 

The Equator System is fixed on the celestial sphere and is well 
adapted for cataloguing purposes. To locate a star by it we need 
only to give its right ascension and declination. That locates it 
permanently and for any place and time. In order for an observer 
to see the object he must calculate in some way where it will be as 
seen from his position at the time he wishes to view it. The Equator 
System is the one actually used in all catalogues. The right ascen- 
sions and declinations are determined essentially as described above. 

The Longitude System is similar to the Equator System in 
that it is fixed on the celestial sphere. If a point is given in terms of 
the celestial latitude and longitude it is uniquely located, but thb 
system is not in so common use as the equatorial because it does not 
connect so easily with the observations made by the telescope fixed 
in the plane of the meridian in connection with the astronomical 
clock. Its principal uses are in describing the positions of the sun, 
moon, and planets, which never depart very far from the ecliptic. 

Determination of Right Ascension of Meridian at Any Time. 
Since the catalogues use the Equator System and the observers 
depend upon the Horizon System, it is necessary in order to use a 
catalogue in making observations to establish the connection between 
the two systems. Suppose the right ascension of a certain star is 
given and it is desired to know whether it is visible at the time in 
question or not. If its right ascension is the same as that of the 
meridian it will be on the meridian and will be visible provided it is 
not too near the southern pole of the sky. On the other hand, if 
its right ascension is 12 hours from that of the meridian it will be on 
the opposite side of the earth and invisible unless it is near the north 
pole of the sky so as to be above the horizon. The right ascension 
of the star being given in the catalogue, the problem of determining 
whether it is visible or not is reduced to that of finding the right 
ascension of the meridian at any time. We shall now consider this 
problem. 

The sun is found by observation to be at the vernal equinox 
on March 21 of each year. (This date may vary by a day because 
of the accumulated errors which are adjusted every four years by the 
leap year.) It moves eastward along the ecliptic at a nearly uniform 
rate, the variation from uniformity being expressed by the law of 
areas. For present purposes it is sufficiently exact to suppose it 



70 



ASTRONOMY 



moves eastward uniformly along the equator, which is represented 
by the circle ME AW in Fig. 33. Since it makes the circuit of the 
heavens in 12 months, and since the circumference is divided into 
24 hours of right ascension, it follows that the sun moves eastward 
from the vernal equinox about two hours each month. Consequently, 
to find the right ascension of the sun, it is necessary only to count the 
number of months from March 21 to the day in question and to 
multiply by two. Thus, on June 21, which is three months after 
the sun passes the vernal equinox, the right ascension of the sun is 
approximately six hours. On October 21, which is approximately 
seven months after the sun passes the vernal equinox, the right 
ascension of the sun is 14 hours. 

We wish, however, the right ascension of the meridian at the 

time in question instead of the 
right ascension of the sun. We 
shall make the determination of 
the right ascension of the sun 
the first step in solving this prob- 
lem. If it is the stars we wish 
to observe they necessarily will 
be seen at night and the most 
convenient time is in the early 
part of the night. Suppose, 
therefore, that as a practical 
problem we determine the right 
ascension of the meridian at 
eight o'clock on any night. By the method described above the 
right ascension of the sun is found, whose position is indicated by s 
in Fig. 33. Now the right ascension is counted eastward. Conse- 
quently, the right ascension of the meridian M is equal to that of 
the sun plus the angular distance sWM . If it is 8 o'clock p. m. the sun 
has passed the meridian eight hours and the arc sWM is eight hours. 
For example, on June 21 the right ascension of the sun is six hours 
and the right ascension of the meridian at 8 P. M. is 6+8= 14 hours. 
If one wished to locate the vernal equinox, which would be less con- 
venient to use, it would be found six hours west of the sun. 

Similarly, on October 21 the right ascension of the sun being 14 
hours, the right ascension of the meridian at 8 p. m. is 22 hours. 




Fig. 33. Determination of the Right 
Ascension of the Meridian 



ASTRONOMY 71 

In the two examples the stars that are on the meridian at the times 
in question are, respectively, those whose right ascensions are 14 hours 
and those whose right ascensions are 22 hours. The problem is 
solved in an exactly similar manner for any other day and time of day. 
Application of Declination to Location of Stars. It is evident 
that the visibility of a group of stars depends not only upon their 
right ascension but also upon their declination. In Fig. 24 it was 
shown that when the sun is north of the equator it is visible more 
than one-half of the 24 hours, while if it is south of the equator it is 
visible less than one-half of the 24 hours. That is, when the sun is 
north of the equator it is visible at a greater distance from the merid- 
ian than it is when it is south ^___^_^ 
of the equator. Since the /^ \ " s\ 
diurnal motion of the sun is par- /A ^- \ x\ 
allel to the diurnal motions of / \ X /\ \ \ 
the stars the same thing is true / \ __-___lVi^___\ \\ 
of them. The difference is that - y' \ /\ ^k N 
the stars always have sensibly ry^*^-— ^ _ y(fiORrzo/i^ ^—~~^\ 
the same declinations and any \\ ^\/ N. \ / 
statement made for them at \ y/ \ \. \ / 
one time holds for all time. ^\\^ \ ^/ 
Another difference is that the ^^^-^Jl_^-^^^ 
stars extend all the way from Fig . 34 . The D iumai Circles of the stars. 

c\r\e> nnlp fr> tV><=» r»+V»AT« 'PViocfi Those near the North Pole are alwavs above 

one poie io me otner. inose the horizon and those near the South Pole 
which are on the equator, half are never visible - 

of which is above the horizon, are visible only if they are less than 
six hours east or west of the meridian. 

For practical observations it is necessary that the stars should 
be some little distance above the horizon, though theoretically they 
are visible until they arrive at the horizon. Stars which are north 
of the equator are visible even though their distances from the merid- 
ian east or west are somewhat greater than six hours, the amount 
depending on how far they are north. In Fig. 34, it is seen that 
those which are near enough the pole, viz, in sector NQP, are always 
visible. The pole P is the center of the diurnal circles and the dis- 
tance NP is equal to the distance PQ. It was shown above that 
NP is equal to the latitude of the observer. Therefore, those stars 
whose distance from the pole of the sky is less than the latitude of 



72 ASTRONOMY 

the observer are always visible to him. Around the southern pole 
of the sky there is a similar region of equal area, SP'R, in which the 
stars are never visible. If a star's declination is so far south that its 
distance from the southern pole is less than the latitude of the obser- 
ver then he will never see it. 

If an observer is at the earth's equator all the stars are visible 
to him in the course of time. Those which are at the poles of the 
heavens are on the north or south horizons. Those which are at 
the celestial equator rise in the east, pass through the zenith, and 
set in the west. But if an observer were at the pole of the earth 
the pole of the heavens would be at his zenith and the celestial 
equator on his horizon. Therefore, only one-half of the celestial 
sphere would ever be visible to him. The diurnal motions of the 
stars would be in circles parallel to the horizon. 

Origin of Constellations. Nearly all our constellations (groups 
of stars) have been handed down to us from prehistoric times. They 
had their origin, probably, in Babylonia and Egypt and were trans- 
mitted to us through the Greeks and the Arabians. Many of the 
names of the stars as well as of the reference points and lines are of 
Arabic origin, having been translated into this tongue from the 
more ancient ones. Thus the words zenith, nadir, horizon, azimuth, 
etc., are Arabic. The names of most of the bright stars are also 
Arabic. Those observers who originally named the constellations 
lived in the northern hemisphere, and there were certain stars in the 
vicinity of the south pole of the sky which were not visible to them. 
Consequently, in this part of the sky the stars were given no names. 
There were also certain places in the northern heavens where the 
stars were not very conspicuous, which were not covered by the con- 
stellations of the ancients. To fill up these gaps a few constella- 
tions have been added in modern times. 

The outlines of the constellations are extremely irregular and 
the stars situated in them generally give no suggestion whatever of 
the names which have been assigned to them. By the wildest 
stretch of the imagination it is not possible for us to see that the stars 
which constitute Leo have any resemblance to the outline of a lion, 
and equally dissimilar to their names are the other constellations. 

A list of the constellations is given in Table I. In the left- 
hand column their right ascensions are given and at the top of the 



TABLE I 
List of Constellations with Right Ascensions and Declinations 





+ 90° to +50° 


+ 50°.to+25° 


+ 25°to0° 


0° to - 25° 


- 25° to - 50° 


+ 50° to - 90° 


I-II 


Cassiopeia 
46 


\ndromeda 

18 
Triangulum 

5 


Pisces 18 
Aries 17 


Cetus 37 


Phoenix 32 
Apparatus 
Sculptoris 13 


(Phoenix) 
Hydrus 18 


III-IV 




Perseus 46 


Taurus 58 


Eridanus 64 


(Eridanus) 


Horologium 

11 
Reticulum 9 




V-VI 


Camelopar- 
dalus 36 


Auriga 35 


Orion 58 
Gemini 33 


Lepus 18 


Columba 15 


Dorado 16 
Pictor 14 
Mons Mensa 
12 


VII-VIII 




Lynx 28 


Canis 

Minor 8 
Cancer 15 


Canis Major 

27 
Monoceros 

12 


Argo Navis 
149 


Fiscis Volans 
9 




IX-X 




Leo Minor 15 


Leo 47 


Hydra 49 
Sextans 5 








XI-XII 


Ursa Major 
53 




Coma Ber- 
inices 20 


Crater 15 
Corvus 8 


Centaurus 6 


Chameleon 
13 




XIII-XIV 




Janes Vena- 

tici 15 
Bo "tes 36 




Virgo 39 


Lupus 34 


Crux 13 






Musca lo 


XV-XVI 


Ursa Minor 
23 


Corona Bo- 

realis 19 

Hercules 65 


Serpens 25 


Libra 23 


Norma 14 


Circinus 10 


XV1I-XVIII 


Draco 80 


Lyra 18 


Aquila 37 
Sagitta 5 


Scorpio 34 
Ophiuchus 
46 


Ara 15 


Triangulum 
Australis 11 

A pus 8 


XIX-XX 




Cygnus 67 


Vulpecula 

23 
Delphinus 

10 


Sagittarius 

48 


Corona 
Australis IS 


Telescopium 

16 
Pavo 37 
Octans 22 




XXI-XXII 


Cepheus 44 


Lacerta 16 


Equuleus 

5 


Capricornus 
22 


Piscis , , ,- 

,. , , Indus l.i 
Australis Id 


XXIII-XXI\ 






Pegasus 
43 


Aquarius 


Grus30 Toucan&22 






36 







74 ASTRONOMY 

columns are their declinations. In connection with each constella- 
tion a number will be observed which indicates the number of con- 
spicuous stars in the constellation. The names of certain constella- 
tions are printed in italics. These are the stars which lie along the 
ecliptic and are called the signs of the zodiac. The ancients always 
spoke of the sun as being in a certain sign or constellation, as in 
Scorpio, Sagittarius, etc. It is easy for us to determine at what time 
of the year the sun is in a given constellation. For example, from 
the list of constellations we see that the right ascension of Scorpio 
is XVII - XVIII hours. The sun has a right ascension of 18 hours 
at 18/2=9 months after March 21, or December 21. 

Suppose it is required to find at what time of the year Leo is 
visible at 8 P. M. From the table it is seen that its right ascension 
is ten hours. If it is to be on the meridian the right ascension of the 
meridian is therefore ten hours on the day in question. The sun 
being eight hours west, and right ascension being counted eastward, 
the right ascension of the sun will be 10—8=2 hours. The right 
ascension of the sun is two hours on April 21. Therefore, the constel- 
lation Leo is on the meridian April 21 at 8 p. m. In this way the 
table can be used to find at what time of the year any constella- 
tion is on the meridian at eight o'clock at night, or at any other 
hour of the night. It should be used in locating the stars, espe- 
cially in connection with the star maps. 

Maps I, II, III, and IV give all the constellations except 
those within 40 degrees of the south pole of the sky, which are 
not visible in the latitude of the United States. Map I shows 
those around the north pole of the heavens. It is made so it can 
be used by determining first the right ascension of the meridian at 
the time in question; and second by turning the map so that this 
hour of right ascension which is marked on its margin, is above the 
pole ; then the map is held up so that its center is seen by the eye in 
the direction of the pole of the sky. When the map is turned around 
in this way to the sky the positions of the stars located on it are the 
same relatively as those in the sky. 

Suppose, for example, that the time the observer uses it is 
May 21, at 8 p.m. The right ascension of the sun on this date is 
four hours, and of the meridian at this time 12 hours. Consequently, 
the hour circle marked 12 in the map must be held directly above 



ASTRONOMY 



75 



MAP 1 

Constellations Around North Pole of the Heavens 




] ST MAGrf/TUDE * 



variable: stah • 

DOUBLE " - 

CLUSTJZFi CI 

POLE °/E-CL/F>TIC • 



* • 




ASTRONOMY 



77 




78 



ASTRONOMY 




ASTRONOMY 79 

its center. As the map is looked at on the page this is the lower 
left-hand part. When this is turned around, so it is up and the map 
held to the sky, it is seen at once that the Big Dipper is above the 
pole, that Cassiopeia is directly below the pole, that Camelo- 
pardalus is to the west of the pole, and that Draco is to the east of it. 
In a similar way it can be used for any other time of the year and 
of the night. 

The other maps give the region along the equator. Consider 
the time May 21, at 8 P. M. The right ascension of the meridian, 
as has been stated, is then 12 hours. It is seen by referring to the 
right ascension marks, which are on the center line of these maps, 
that Map III must be used in this case. The mark XII is found 
on this map where the ecliptic crosses the equator from north to 
south. If the map is held up to the southern sky, so that this point 
is on the meridian at the height of the equator, then the stars will be 
spread out relatively on the map the same as they are on the sky. 
It will be seen then that Leo is a little west of the meridian and a 
little higher than the equator. On the meridian south of the equa- 
tor and a little to the west is the constellation Crater. On the 
meridian and a little west of it, running across the equator, is the 
zodiacal constellation Virgo. Five hours east of the meridian and 
30 degrees south of it is the constellation Scorpio. Consequently, 
on this date and at this time of day Scorpio should be seen just ris- 
ing in the southeastern sky. In this manner these maps can be used 
for any day in the year and any time of the day. The constellations 
and the maps together give one the means of locating any group 
of stars he wishes at any time whatever. 

Naming the Stars. The brightest star in all the sky is called 
Sirius. There are also Vega, Aldebaran, Arcturus, etc. But since 
the number of stars visible to the unaided eye is about 5,000 and 
the number within the reach of our telescopes runs up into the mil- 
lions, it is obvious that it would be a difficult problem to have names 
for all of them. As a matter of fact only a relatively small number 
have actually been given names. 

One of the methods of designating the stars, besides giving them 
names, is by stating in what constellation they are to be found 
and their rank in the constellation in order of brightness. The 
brightest star in a constellation is called Alpha, a Greek letter, the 



80 ASTRONOMY 

second, Beta, etc. The name of the constellation is put after the 
Alpha, Beta, etc., in the genitive case. For example, according 
to this system of designating the stars the brightest star in the con- 
stellation Leo is called Alpha Leonis, and the brightest star in Cygnus 
(the Swan) is called Alpha Cygni. But since there are only 24 
letters in the Greek alphabet it is obvious that this method has its 
limitations. After the Greek letters are exhausted the Roman letters 
are sometimes used. But the list of Roman letters is also limited, 
and in a constellation having thousands of stars this method is 
obviously entirely inadequate. 

Another method, adopted by the English observer, Flamsteed, 
about 1700, is to number all the stars in each constellation accord- 
ing to their right ascension. Thus Xo. 1 in Leo would be that star 
in the Lion which is farthest west; that is, whose right ascension is 
the least. The objection to this method is that the numbering has 
no relation whatever to the magnitudes and depends upon a very 
arbitrary and irregular division of the whole sky into constella- 
tions. If, after a catalogue is made, new stars should be added, it 
would be necessary to re-number all of those which had a greater 
right ascension. 

Still another method of designating the stars is to give their num- 
ber in a certain catalogue irrespective of the constellation in which 
they appear. The stars in these catalogues are often arranged and 
numbered in the order of their right ascension. While this system 
has no relation to their magnitudes, it depends upon their positions 
in the sky and is convenient when one wishes to make an observing 
program. If a certain star will be visible on a certain evening at a 
convenient time for observation, then all of those whose numbers are 
near it will also be visible at the same time. The fact that they are 
north or south of it makes no important difference unless, indeed, 
they are so far south as to be always invisible. 

Star Catalogues. The earliest star catalogue of which we have 
any record is a catalogue of 1,080 stars made by Hipparchus for the 
epoch 125 b. c. It was inspired by the appearance of what is called 
a temporary star. In a region of the sky in which no star had before 
that time been visible a brilliant star suddenly blazed out and after 
a few months disappeared. Hipparchus was astonished by the 
phenomenon since nearly all the stars are always the same. He 



ASTRONOMY 81 

determined then to make a catalogue of all the brightest stars, 
giving their positions in order that later astronomers might be able 
to determine whether they were appearing and disappearing and 
whether they were changing their positions in the sky. This cata- 
logue of Hipparchus was revised and reduced to the epoch 150 a.d. 
by the astronomer Ptolemy. 




Fig. 35. Photograph of a Part of the Constellation Taurus Showing the Hyades near 
the Top of the Picture 

Tycho Brahe, who has been mentioned as being a great observer, 
in 1580 made a catalogue of 1,0,15 stars. Since that time star cata- 
logues have been very numerous. 

One of the greatest made by direct telescopic observations is 
that of Argelander (1799-1875) which contains 324, 19S stars. While 
only about 5,000 stars are visible to the unaided eye, Argelander 



82 ASTRONOMY 

made his catalogue with a telescope 2.5 inches in diameter. There 
are many catalogues containing from a few hundred to a few thousand 
stars whose positions are given with the very highest degree of 
precision. They are useful in determining with great accuracy the 
positions of the heavenly bodies which move, such as the planets 
and comets; for it is only necessary to locate a wandering body 
with respect to the known fixed stars in order to have its 
position. 

Recently an enormous catalogue made by another plan has been 
projected and nearly completed. It was found in 1882 that the stars 
could be photographed. This suggested to the English astronomer 
Gill the making of a catalogue of the whole sky by the photographic 
process. A photograph of a region is taken and on the photographic 
plate there will be the images of some stars whose positions are 
already known. When the distances and directions of the unknown 
stars from the known stars are measured, their positions become 
known. The work of making this great catalogue was undertaken 
by international co-operation and the work was divided among many 
observatories. Necessarily some photographs had to be taken from 
points on the earth north of its equator and others from places south 
of its equator. Each plate covers about four square degrees of sky, 
and since they must overlap in order to connect with one another, 
and since it is advisable to have the whole sky covered twice, nearly 
22,000 plates are required. On these plates about 15,000,000 of stars 
will be shown. Many of them will be very faint and it is at present 
planned to measure and catalogue only 1,500,000 of them. Fig. 35 
is a photograph of a region in the constellation Taurus and includes 
the stars known as the Hyades, which can be seen as a little cluster 
near the top of the picture. 

Magnitudes of Stars. The quantity of light we receive from 
the different stars differs greatly, and probably we do not get precisely 
the same light in quantity and quality from any two stars. The 
magnitude of a star refers to the quantity of light we receive from 
it and has no necessary relation to its actual size or brilliance. A 
rather faint star near us would give us more light than a much larger 
one farther away. The stars which can be seen without the aid of a 
telescope are divided arbitrarily into six groups. The 20 brightest 
stars constitute the first group, and the average of the 20 brightest is 



ASTRONOMY 83 

the ideal first-magnitude star. The faintest stars that can be seen 
without a telescope are the sixth-magnitude group. 

It is found by observations that a first-magnitude star gives us 
100 times as much light as a sixth-magnitude star. Of course, what 
is a sixth-magnitude star depends somewhat upon the sensitiveness 
of the eye of the observer if it is defined as the faintest star which 
can be seen without a telescope. It also depends upon various other 
factors, such as the transparency of the atmosphere and the presence 
or absence of moonlight or artificial light. But those stars which are 
ris as bright as the ideal first-magnitude star are at least near the 
limits of visibility under ordinary conditions, and are taken as the 
stars of the sixth magnitude. If the ratio of light of the first-magni- 
tude star to the sixth-magnitude star is as 100 to one, it is found in 
order that the ratios from the first to the second, the second to the 
third, and so on, shall all be equal, that the ratio of the light from a 
first-magnitude star to that from a second-magnitude star is as 2.512 
to 1; and, in general, the ratio of the light received from any star 
to one in the next group fainter is this same number. 

The stars next fainter than those which are visible without a 
telescope constitute the seventh-magnitude group. Then follow the 
eighth, ninth, and so on. The faintest stars which are in reach of 
our best modern instruments are of about the seventeenth mag- 
nitude. 

If a star is brighter than the ideal first-magnitude star its magni- 
tude is taken as less than one. For example, the star Vega, being 
brighter than the ideal first-magnitude star, has a magnitude 0.2; 
and the brightest star in the sky, Sirius, has a magnitude —1.4. In 
describing the magnitudes of the stars it is necessary to use decimals 
in order to attain a considerable degree of accuracy because the stars 
do not fall into the ideal groups. There are many between the exact 
first and the exact second magnitudes, and so on, for all other even 
magnitudes. The star Vega is brighter than the first-magnitude star 
but not a full magnitude brighter. Consequently, its magnitude is 
not 0.0, which would be a full magnitude brighter, but 0.2. The 
star Sirius is more than one magnitude brighter than Vega and going 
beyond the 0.0 has to be represented by a negative number It is 
2.4 magnitudes brighter than the ideal first-magnitude star. On this 
basis the magnitude of the sun is approximately —20. 



84 



ASTRONOMY 



TABLE II 
List of First- Magnitude Stars 



Star 


Magni- 
tude 


Right 
Ascension 


Declination 


Color 


When on 
Meridian 
at S p. m. 


Sirius 


-1.4 


6hr.40 m. 


-16° 34' 


Bluish white 


July 1 


(Greater Dog) 














Arcturus 


0.0 


14 


10 


+ 19 48 


Orange 


Oct. 24 


(Bootes) 














Vega 


0.2 


18 


33 


+38 40 


Pale blue 


Jan. 1 


(Lyra) 














Capella 


0.2 


5 


8 


+45 52 


Yellowish 


June 6 


(Auriga) 














Rigel 


0.3 


5 


9 


- 8 20 


White 


June 6 


(Orion) 














Canopus 


0.4 


6 


21 


-52 38 


Bluish 


June 26 


(Argo) 














Procyon 


0.5 


7 


33 


+ 5 32 


White 


July 12 


(Smaller Dog) 














Betelgeuse 


0.9 


5 


49 


+ 7 23 


Ruddy 


June 17 


(Orion) 














Alpha Centauri 


1.0 


14 


31 


-60 20 


White 


Oct, 28 


Achernar 


1.0 


1 


33 


-57 51 


White 


April 11 


(Eridanus) 




• 










Altair 


1.0 


19 


45 


+ 8 33 


Yellowish 


Jan. 17 


(Aquila) 














Aldebaran 


1.0 


4 


30 


+ 16 16 


Red 


May 28 


(Taurus) 














Antares 


1.1 


16 


22 


-26 10 


Deep red 


Nov. 27 


(Scorpio) 














Pollux 


1.1 


7 


38 


+28 19 


Orange 


July 15 


(Gemini) 














Spica 


1.2 


13 


19 


-10 32 


W T hite 


Oct. 11 


(Virgo) 














Beta Centauri 


1.2 


13 


55 


-59 48 


White 


Oct. 20 


Alpha Crucis 


1.3 


12 


20 


-62 26 


Bluish white 


Sept. 26 


Fomalhaut 


1.3 


22 


52 


-30 16 


Ruddy 


March 5 


(Piscis Australis) 














Regulus 


1.4 


10 


2 


+ 12 33 


White 


Aug. 21 


(Leo) 














Deneb 


1.4 


20 


38 


+44 53 


White 


Feb. 1 


((Jygnus) 




1 











It is easy to get a general idea of the relative brightness of stars 
separated by any magnitude. Suppose, for example, we wish to find 
how much brighter stars of the first magnitude are than those of the 
seventeenth. As has been stated, stars of the first magnitude are 
100 times brighter than those of the sixth; similarly, those of the 
sixth magnitude are 100 times brighter than those of the eleventh. 
Therefore, the stars of the first magnitude are 100 2 = 10,000 times 
brighter than those of the eleventh. Those of the eleventh magnitude 
are 100 times brighter than those of the sixteenth. Consequently, 
the stars of the first magnitude are 10,000X100=1,000,000 times 
brighter than those of the sixteenth magnitude. Those of the sixteenth 



ASTRONOMY 



85 



TABLE III 
Number of Stars Visible to Naked Eye 



First magnitude 20 

Second magnitude 65 

Third magnitude 190 



Fourth magnitude 425 

Fifth magnitude 1100 

Sixth magnitude . 3200 



magnitude are 2.5 times brighter than those of the seventeenth. 
Therefore, we have for the final result that stars of the first magni- 
tude are 2,500,000 times brighter than those of the seventeenth. 
Those of the sixth magnitude are 25,000 times brighter than those of 
the seventeenth. These results give an idea of the relative power of 
our modern instruments compared to that of the unaided eye. 
Computing the relative brightness of the sun in the same way, we 
find, under the hypothesis that its magnitude is - 26, that it is in 
round numbers 60,000,000,000 times brighter than the ideal first- 
magnitude star. 

First=Magnitude Stars. The twenty stars that constitute the 
first-magnitude group are conspicuous objects in the heavens which 
always keep their positions relative to the others. They serve as 
guideposts for a study of the constellations, and those which are 
visible in the latitude of the observer should be familiar to him. 
They are distinguishable by their brightness, their color, and their 
relations to fainter stars near them. A table of the first-magnitude 
stars is given herewith, including also in the second column their 
magnitudes; in the third, their right ascensions; in the fourth, their 
declinations; in the fifth, their colors; and in the sixth, the times of 
year at which they cross the meridian at 8 p.m. The names of the 
constellations to which the stars belong are given in parenthesis 
under their proper names, except in those cases where the stars have 
no special names. From the principles which have been explained 
above, it is a relatively simple matter to find their approximate 
positions in the sky at any time and, by means of Table II, to 
locate them. When they have once been located and carefully 
observed for their own peculiarities and relations to neighboring 
stars, they will not be forgotten. 

Number of Stars. It is a common impression that the stars 
which are visible to the unaided eye are absolutely numberless, and 
they are often compared to the grains of sand on the seashore. As 




Fig. 36. Star Cloud in Sagittarius Photographed by Barnard 



ASTRONOMY 87 

a matter of fact, they are not only finite in number, but their number 
is not very great. In Table III is given the number of stars in the 
whole sky in the first six magnitudes. 

It is seen that the whole number of stars in all the sky visible 
without telescope is 5,000. At any one time fewer than half of these 
are visible because only one-half of the sky is above the horizon, and 
those faint stars whose light must come through the denser atmos- 
phere near the horizon are not visible. 

It will be noticed from Table III that each fainter magnitude 
has approximately three times as many stars as the preceding one. 
If this ratio continues it is found by calculation that there are about 
200,000 stars in the first nine magnitudes, and the actual observa- 
tions are in harmony with this computation. If the ratio kept up 
indefinitely there would be infinitely many stars. But beyond the 
ninth magnitude it begins to fall off, so that each fainter group has 
fewer than three times as many stars in it as are in the preceding 
group. It is not known with any high degree of accuracy how many 
stars there are in the first 17 magnitudes, which are within the range 
of the most powerful telescopes, but from counts of many representa- 
tive regions it is concluded that there are probably more than 
100,000,000 of them. Fig. 36 is a photograph of a portion of a 
part of the great star cloud in Sagittarius. This bright part of the 
Milky Way is in the southern sky in the early evening in mid-summer. 

Proper Motions of Stars. The stars are called "fixed," and 
the fainter ones are the most nearly fixed of anything we know. 
Yet they are not absolutely fixed. They move slowly with respect 
to one another, and with accurate instruments it is possible in many 
cases to detect these changes in a relatively short time. The motions 
of the stars relatively to one another, or rather their motions with 
respect to the ideal, fixed right ascension and declination circles, are 
called their proper motions. The greatest proper motion known is 
only 8.7 seconds per year. Most of the stars move less than one 
second per century. The smallness of this greatest motion of S.7 
seconds per year is illustrated by the fact that it would take this 
star 220 years to travel over an arc equal to the apparent diameter 
of the moon. This star is of the eighth magnitude and is therefore 
invisible to the unaided eye. The proper motions of all visible stars 
are so small that the sky appears to us almost as it did to the ancient 



88 ASTRONOMY 

Babylonians who first named the constellations. They looked up 
into the night sky and saw the Big Dipper, the Pleiades, Orion, etc., 
shining with almost the same luster as that with w T hich these splendid 
stars shine at the present time, and situated relatively to one another 
sensibly as they are now. 

The proper motions of the stars are, of course, due to their 
actual motions. The sun, being a star also, has an actual motion 
through space. It is moving nearly toward the star Vega at the rate 
of 400,000,000 miles per year, or at the rate of 12 miles per second. 
The motions of the stars toward us or from us are determined by 
means of the spectroscope. It is found from those which so far have 
been observed by means of the spectroscope (only those of the eighth 
magnitude or brighter), that on the average they move at the rate 
of about 20 miles per second, or about 700,000,000 miles per year. 
One might imagine at first thought that, if a star were coming toward 
us at the rate of 700,000,000 miles per year, or at the much greater 
rate at which some of the stars move, it would speedily become 
brighter, and that if it were receding, it would diminish in brilliance. 
The fact is, however, that their distances are so great that these 
changes do not alter their apparent magnitudes by sensible quan- 
tities in. the course of the few centuries or, at the most, the few 
thousand years, they have been under observation. 

The Milky Way or Galaxy. There is a band of hazy light, 
averaging about 20 degrees in width, stretching around the sky in 
approximately a great circle. A keen eye, under good circumstances, 
can see that it is made up, at least in its coarser parts, of fine stars, 
and it was commonly supposed by the ancient Greeks that it was a 
vast aggregation of stars so minute that they were not individually 
distinguishable. The Pawnee Indians of our western plains have 
the curious story that it is a cloud of dust made by a buffalo and 
horse racing across the sky. For a long distance it presents a length- 
wise division. They thought the horse ran on one side, where the 
stars are a little larger, and kicked up a coarse dust; and that the 
buffalo ran on the other side and kicked up a fine dust, which con- 
stitutes the part whose individual stars are beyond visibility. 

The Milky Way runs diagonally across the sky; that is, it does 
not follow an hour circle or a declination circle. It crosses the 
equator at points whose right ascensions are about 7 hours and 19 




Fig. 37. 



Dark Lanes" in the Star Clouds in Ophiuchus, Photographed by Barnard at 
the Yerkcs Observatory 



90 ASTRONOMY 

hours, and its inclination to the equator is about 63 degrees. The 
north pole of the Galaxy has a right ascension of about 13 hours 
and a declination of 27 degrees. It is extremely irregular in outline, 
having many dense star clouds and at other places dark holes and 
dark rifts across it. Fig. 37 is a photograph of a portion of the Milky 
Way in Ophiuchus, showing star clouds, nebulas, and dark lanes. 

How to Find the Pole Star. The most conspicuous group of 
stars in the northern heavens which is' always visible to observers of 
our latitude, is the Great Dipper. Everyone who knows any stars at 
all is familiar with this group. Its outline is perfectly definite and is 
made up of seven stars of about equal magnitude — the second. 
When the Dipper has been located it is easy to find the pole star. 
Start at the bottom of the bowl of the Dipper on the side opposite 
the handle, go along the edge of the Dipper opposite the side of the 
handle and continue about five times the distance between these 
two stars, and the pole star is reached. The two stars in the Dipper 
in the side opposite the handle are called the "Pointers," for they 
are almost exactly in a line with the pole star. Knowing this fact 
and the distance of the pole star from them compared to their dis- 
tance apart, it is always easy to locate it. It is near no other bright 
star and is itself of the second magnitude. Since it is always visible in 
the northern hemisphere it serves as a unit for determining the magni- 
tudes of stars whose brightness is approximately equal to that of itself. 

In describing the positions of stars it is extremely convenient 
to say that one is in a certain direction and distant a certain number 
of degrees from a known star. Ordinarily, a person has a vague 
idea of the distance covered by 20 degrees on the sky, for he knows the 
whole circumference is divided into 360 degrees. Therefore, it is 
useful to have in mind a number of distances between stars for use 
as units. One convenient unit is the altitude of the pole star above 
the horizon. It was shown above that it is equal to the latitude of 
the observer. Consequently, if the observer's latitude were 40 
degrees the altitude of the pole star would be 40 degrees. This gives 
a means of estimating distances of about 40 degrees. An error is 
likely to creep in because the distance from the horizon in a ver- 
tical direction from the pole star generally seems somewhat different 
from a distance of 40 degrees between two stars which are not on a 
vertical circle. The distance between the Pointers in the Big Dipper 



ASTRONOMY 91 

is approximately five degrees. This serves as a very convenient 
unit for measuring the small distances. The distance between the 
stars at the bottom of the Big Dipper is seven degrees. And the 
distance from the Pointer nearest the pole to the pole star is 28 degrees. 

Fig. 38 gives an outline map of the Big Dipper and the pole star 
with the names of the stars. In this case the scheme of naming the 
brightest star in the constellation Alpha, the next brightest Beta, 
and so on, is not followed. The star Zeta at the bend in the handle 
of the Big Dipper, which was called Mizar by the Arabs, has a very 
faint star near it called Alcor, which means "the test." The Arabs 
considered the eyes of a person good if he could see this faint test 
star. The difficulties of seeing it are due 
to the fact that it is near the bright star 
Mizar and is itself faint. This star should 
be looked for and it will be found that 
every one can easily see it whose eyes are 
considered anywhere near normal. 

The star Alcor is of the fifth mag- 
nitude and its distance from Mizar is 

11.5 minutes of arc. The shortest dis- 
tance between two stars which are visi- 
ble as distinct objects without telescopic 

aid, is about three minutes. With a tel- Fi e- 38. The Big Dipper and 

' ... the Pole Star 

escope it is found that Mizar itself is a 

fine double, composed of a white star and one of an emerald 

color. The distance of the two components from each other is about 

14.6 seconds of arc, and a 3-inch telescope will easily show them. 
It is not to be inferred that the two suns which compose this system 
are really very close together because they appear close together. 
This apparent nearness is the consequence of their vast distance from 
us. It is not known just how far they are away but almost cer- 
tainly it takes their light more than 100 years to come to us. The 
meaning of this statement becomes apparent when one remembers 
that light travels at the rate of 186,330 miles per second. 

The brighter component of Mizar was found to be a double by 
the use of the spectroscope in 1889*. This discovery by Professor E. C. 
Pickering was the first of its kind. A spectroscopic binary is one in 
which the two components are so close and their distance from us 




92 ASTRONOMY 

so great that they are not visible as separate objects with any tele- 
scope. But by an adaptation of the spectroscope, whose description 
will be deferred, it is possible under certain circumstances to deter- 
mine their binary character. Not only this, but in the case of the 
spectroscopic binaries it is possible to find out other things about 
the system, particularly the actual distance of the stars apart and 
their combined mass. In the case of the brighter component of Mizar 
the stars perform a revolution about their center of gravity in 20.5 
days and are at a distance of 25,000,000 miles from each other. Their 
combined mass is about five times that of our sun. 

The pole star is also an object of much interest. It is found to 
be a double star having a faint companion of the ninth magnitude 
at a distance from it of about 18.5 seconds. The component can be 
seen with a 5-inch telescope using a magnifying power of from 75 
to 100 diameters. The larger one of the two components was found 
in 1899 to be a spectroscopic binary. This group of stars is so far 
from us that 40 years are required for its light to come to us; that 
is, we see it as it was 40 years ago. 

Cassiopeia. The right ascension of this constellation is about zero 
hours. Consequently, it is on the meridian at 8 p. M. November 21. 
But if one wishes to find it without referring to its right ascension 
and declination it can be located by going from the Great Dipper 
through the North Star and as far beyond as that distance. It is, 
therefore, above the pole when the Dipper is directly below. Cas- 
siopeia is distinguished by a zigzag, or letter W, composed of stars 
from the second to the fourth magnitude. The brightest star is at 
the bottom of the second part of the W. This is found to be a fine 
double star whose colors are rose and blue, and it can be seen sepa- 
rately with a 2-inch telescope. 

One of the most interesting objects in the constellation of 
Cassiopeia is the star Eta, which is near the middle of the third stroke 
of the W, and about two degrees from the brightest star. It is a fine 
double star and can be separated with a 3-inch telescope. These 
two stars form a physical system and revolve around their center of 
gravity in a period of about 200 years. They are so far away that 
it takes their light about nine years to come to us. 

In the constellation Cassiopeia a temporary star suddenly 
appeared in 1572. Its dazzling splendor and the fact that it had 



ASTRONOMY 93 

recently appeared, attracted the attention of Tycho Brahe who was 
then a young man, and turned his attention to astronomy. 

The Equinoxes. It is possible to find the positions of the 
equinoxes by means of the processes described above, but it is also 
possible to locate them easily by direct observations of the stars. 

To find the vernal equinox, draw a line from Polaris through the 
most westerly star in the W of Cassiopeia and prolong it 90 degrees. 
The point where it strikes the equator is the vernal equinox. The 
autumnal equinox is obtained by drawing a line from Polaris through 
Delta Ursse Majoris and prolonging it until it strikes the equator. 
This point is in the constellation Virgo about 10 degrees north and 
20 degrees west of the first-magnitude star Spica. 

Lyra. Lyra (the Lyre) is a small constellation but one of the 
most interesting of them all. Its mean right ascension is about 18.7 
hours and its declination is about +40 degrees. It is conspicuous 
because of the brilliant first-magnitude star Vega which is in it. 

It was explained in connection with the discussion of the pre- 
cession of the equinoxes, that the plane of the earth's equator slowly 
shifts on account of the attraction of the moon and sun on the earth's 
equatorial bulge. This causes the axis of the earth to point con- 
tinually in different directions. The pole of the sky is the point on 
the celestial sphere toward which the axis of the earth is directed. 
On account of the precession of the equinoxes the position of the pole 
of the sky is continually changing. It describes a circle whose radius 
is 23.5 degrees and whose center is the pole of the ecliptic, in a period 
of 26,000 years. It happens that this circle which the celestial pole 
describes passes very near the star Vega. In 12,000 years from now 
the pole will be very near Vega and at this time that star .will be the 
pole star. How much more glorious and conspicuous an object it 
will be than Polaris! 

Lyra is also a constellation of interest because it is nearly in 
that direction that the sun with its planets is moving. 

There are two stars of the fourth magnitude, Epsilon and Zeta 
Lyrae, each about two degrees from Vega. One is northeast and the 
other southeast, and with Vega they form a nearly equilateral 
triangle. The star Epsilon is a close double, composed of two nearly 
equal stars separated by a distance of 207 seconds of arc. It is a 
famous test object for observation without optical aid. A person 



94 ASTRONOMY 

with good eyes and under favorable atmospheric conditions in the 
absence of sky illumination can see the two components as separate 
objects. It is worthy of note that it never was known to be a double, 
so far as the records show, until after the invention of the telescope. 
If it is beyond the visibility of an observer he can usually see it with 
the aid of opera glasses. The object does not lose its interest when 




Fig. 39. The Ring Nebula in Lyra 

viewed through a telescope. When examined under considerable 
optical power the two components, which are on the limits of visi- 
bility with the unaided eye, are seen to be very far apart, and each 
one of them is found itself to be a double. Thus, that which, at 
least at first glance, seems to be a single faint star in the sky, when 
examined with a powerful instrument, turns out to be a system of 
four magnificent suns. 



ASTRONOMY 



95 



Another interesting object in this constellation is the ring 
nebula. (See Fig. 39.) 

Scorpio. Scorpio (the Scorpion) is the ninth zodiacal constella- 
tion and the most brilliant of all. In fact, it is one of the finest 
southern constellations that can be seen in our latitude. It is always 
easily recognized by the fiery red first-magnitude star Antares which 




Fig. 40. Thr Great Star Cluster in Scorpio 

in light-giving power is equal to 900 suns such as our own. About 
five degrees northwest of Antares is a very compact and fine cluster 
of stars in which about 5,000 of these objects are crowded in a 
region apparently one-fifth the size of the moon. (See Fig. 40.) 

Bootes. Bootes (the Hunter) is a large constellation reaching 
from near the equator to within 35 degrees of the pole, and having 
a mean right ascension of about 15 hours. The most conspicuous 



96 ASTRONOMY 

object in it is the brilliant orange-colored, first magnitude star Arc- 
turus. This star is approaching us at the rate of about five miles a 
second, but it is so far away that it takes its light 100 years to come 
to us. Its light-giving power is about 1,300 times that of our sun. 

Leo. Leo (the Lion) is another one of the zodiacal constellations 
and the ecliptic passes very near to its brightest star, Regulus. It 
is about 60 degrees west of Arcturus and is easily recognized by a 
sickle of seven stars opening to the southwest, with Regulus at the 




Fig. 41. Photograph or the Pleiades — the "Seven Sisters" — Made at the Yerkes Observatory 

end of its handle. One of the many things of interest in connection 
with this constellation is that the November meteors seem to radiate 
from it. 

Taurus. Taurus (the Bull) contains the Pleiades, the Hyades, 
and Aldebaran. The Pleiades include seven fourth-magnitude stars 
forming roughly a small dipper, and are mentioned in the sacred 
writings and the folk-lore stories of primitive peoples more often 
than any other group of stars in the sky. The ancient Greeks called 
them the "seven sisters" and had a story of how one was later lost. 
Apparently, those who wrote about them at that date were able to 
see only six. Now seven are easily visible to anyone of good eyesight 
under favorable conditions, and to those with more acute vision, 
under the best circumstances, ten or eleven are visible. 



ASTRONOMY 97 

In Fig. 41 is given a photograph of the Pleiades together with 
many stars which can be seen only with optical aid. While the 
Pleiades appear to be small insignificant objects in the heavens they 
are, as a matter of fact, giant suns. Those brighter ones which can 
be seen without a telescope are from 200 to 300 times as great in 
light-giving power as our own sun. They are so far away that, 
according to the discussion of Newcomb, it takes their light 267 
years to come to us. At one time a German astronomer, Maedler, 
supposed that Alcyone, the brightest star of this group, was in the 
center of the universe. This idea has been abandoned as there is no 
evidence whatever to support it. The ecliptic passes about four 
degrees south of the Pleiades. Consequently, the sun, moon, and 
planets pass near it, and in fact the moon sometimes eclipses these 
stars. 

The Hyades are a large and diffuse group of stars which have 
been found by recent observations of Boss to be moving with about 
equal speed toward a distant point in the sky. This, of course, does 
not necessarily mean that they are going to collide . in the remote 
future. But the parallelism of their motion and the equality of 
their speed shows that beyond question they have had a common 
origin. The examinations of them with the spectroscope, which is 
an instrument that enables us to determine the chemical constitution 
of luminous bodies, shows that these stars are very much alike in 
their constitution, a fact which also points to a common origin for 
them. 

Orion. South of Taurus is the constellation Orion, lying across 
the equator between the fifth and sixth hours of right ascension. 
This is one of the finest regions in the whole heavens for a study 
without a telescope. In the winter months, in the early evening, it 
is seen in the southeastern and southern sky. In the northern part 
of it is the ruddy star Betelgeuse, and about 20 degrees southwest 
is the first-magnitude star Rigel. About midway between them and 
almost on the equator is a row of second-magnitude stars running 
northwest and southeast (in Fig. 42 these stars are a little above 
and to the left of the center), which constitutes the belt of Orion. 
From the southern end of this line of three stars are three fainter 
ones going off toward the southwest. These constitute the sword of 
Orion. Careful observation shows that the center of these three is a 



98 ASTRONOMY 

little fuzzy. It is, in fact, one of the most magnificent spectacles in 
the whole sky, the Orion nebula. Fig. 43 shows this splendid object 
as revealed by our most powerful photographic telescopes. 




Fig. 42. The Belt and Sword of Orion and the Brilliant Rigel 

The stars in this part of the sky are exceptionally large and 
remote from us. The star Rigel, shown at the right in Fig. 42, in 
light-giving power is equal to 10,000 such suns as ours. 






: '%Mf* 



1 



100 ASTRONOMY 

Canis Major. Canis Major (the Greater Dog) is a constellation 
southeast of Orion and contains the brightest star in the whole sky, 
Sirius. The brightness of this star depends to a considerable extent 
upon the fact that it is relatively near to us. It takes the light from 
it 8.4 years to come to the earth. Expressed otherwise the star is 
47,000,000,000,000 miles distant from us, and it is approaching us at 
the rate of about 10 miles per second. Sirius is really overtaking the 
sun, for the solar system is actually moving in almost exactly the 
opposite direction. 

It was found in 1862 that the star Sirius had a very faint and 
distant companion. Observations since that time have shown that 
the two revolve around their common center of gravity in a period 
of about 50 years. The distance of the two components from each 
other is about 1,800,000,000 miles. A remarkable fact is that Sirius 
is 10,000 times as bright as its companion, while its mass is little 
more than twice that of its companion. Their combined mass is a 
little more than 3.5 times that of the sun, and they radiate about 30 
times as much light as the sun. 

Gemini. Gemini (the Twins) is the fourth zodiacal constellation 
and is noteworthy for its two principal stars, Castor and Pollux. 
In fact, the constellation gets its name from these two objects (twin 
stars), which are of nearly the same size and about 4.5 degrees apart. 
Castor is the one of the two which is farther north. In ancient 
times Castor seems to have been a little brighter than Pollux, but 
now the condition is reversed. This may be due to the fact that 
Castor is receding from us at the rate of 4.5 miles per second, while 
Pollux is approaching at the rate of 30 miles per second. With this 
large relative velocity of nearly 35 miles per second, over 2,000 years 
have been required for any conspicuous change in their relative 
brightness to take place. 

TIME 

Definition of Equal Intervals of Time. It is very difficult, if 
not impossible, to give a definition of time itself. So far as we, as 
thinking beings, are concerned, the amount of time which passes 
depends upon our intellectual activity in the interval. As an illus- 
tration, it may be mentioned that if we have many new intellectual 
experiences, as for example when we travel, the time seems long; 



ASTRONOMY 101 

while when our activities are in their customary routine, time seems 
to speed rapidly. The same thing is illustrated by the well-known 
fact that a year seems much longer to a young person, to whom the 
experiences of the world are largely new, than it does to an older 
person, whose habits of life have become fixed and whose new experi- 
ences are not numerous. Clearly, however, it is impossible to define 
the length of time by means of the varying mental activities of any 
individual or group of individuals. 

The first law of motion previously given states that a body 
subject to no force moves with uniform speed in a straight line. 
Therefore, by definition, it follows as a consequence of this law, or 
axiom, that two intervals of time are equal if a body, subject to no 
force, passes over equal distances in them. This is the definition of 
the equality of two intervals. In the long run it is found that our 
mental experiences are sensibly in harmony with it. 

The difficulty in applying the definition to find out whether 
two intervals of time are equal, or what amounts to the same thing 
— the relation of two intervals — arises from the fact that it is prac- 
tically impossible to find a moving body subject to no force and to 
bring it under observation. Because of this difficulty an indirect 
consequence of the laws of motion is used. It follows from them, 
as was explained above, that if the earth is subject to no exterior 
forces it will rotate with uniform speed. The character of the forces 
which modify its rate of rotation were discussed in connection with 
its rotation. It was seen that it rotates with sensibly uniform speed, 
and consequently it can be taken as the actual means of measuring 
intervals of time. Using the rotation of the earth as a measure, we 
agree that if the earth turns through equal angles in two intervals of 
time, then the two intervals are equal. The rotation of the earth 
makes the sky turn apparently from west to east. Consequently 
two intervals are equal if the sky, in its apparent motion, turns 
through equal angles in them. The rotation of the earth is the actual, 
fundamental means of measuring time, and clocks are regulated by 
it. The observations depend upon the stars and for this reason the 
discussion of this topic appropriately is taken up here after a discus- 
sion of the rotation of the earth and a description of the constellations. 

Sidereal Time. Sidereal time is time measured by the rotation 
of the earth with respect to the stars; or, by the apparent motion 



102 ASTRONOMY 

of the stars around the earth. A sidereal day is the time it takes 
a meridian of the earth to move from a given position among the 
fixed stars around eastward to the same position again; or, thinking 
of the stars as moving, at least apparently, it is the interval required 
for the fixed stars to pass from the meridian around the earth and 
back to it again. 

The sidereal day is divided into 24 sidereal hours, a sidereal hour 
into 60 sidereal minutes, and a sidereal minute into 60 sidereal seconds. 

Solar Time. Our activities are largely regulated by the day 
and night. Consequently, time for practical purposes should depend 
upon the apparent motion of the sun around the earth rather than 
that of the stars. It is clear that since the sun moves eastward 
among the stars about one degree daily in its apparent annual motion 
around the heavens, the diurnal motions of the stars and sun are 
different. Solar time is time measured with reference to the sun. 
The solar day is the time it takes the meridian to pass from the sun 
eastward around to the sun again; or, the time it takes the sun to 
pass from the meridian apparently around westward back to the 
meridian again. 

Solar days and sidereal days are not of equal length, the solar 
days being nearly four minutes longer. This is easily understood 
from the fact that the sun moves eastward among the stars. Sup- 
pose the meridian is in conjunction with the sun and certain stars, 
and that it moves eastward and around to the same stars again. 
This interval constitutes a sidereal day. In the meantime, how- 
ever, the sun will have moved eastward about one degree and the 
meridian must overtake it before the end of the solar day. There- 
fore, the solar day is longer than the sidereal day, and the difference 
is the time it takes the earth to rotate about one degree. The earth 
rotates 360 degrees in 24 hours, or 15 degrees in one hour. There- 
fore, it will rotate one degree in one fifteenth of an hour, or in four 
minutes. That is, the solar day is about four minutes longer than 
the sidereal day. 

In Fig. 44, let S represent the sun and E 1 the position of the 
earth at one time. Consider the meridian m, which is on the side 
toward the sun, and the distant star s. Suppose that in one sidereal 
day the earth moves forward to E 2 (of course, the distance traveled 
is greatly exaggerated in the figure). This means that the meridian 



ASTRONOMY 103 

m is on the side toward the star again. It is clear from the figure 
that the earth must turn through the angle a which is equal to the 
angle which it has moved forward in its orbit, in order to bring m 
in line with the sun. This shows why the solar day is longer than 
the sidereal day. 

Mean Solar Time. It has been stated above that the sidereal 
days are all of the same length and that the solar days are longer 
than the sidereal because of the earth's motion forward in its orbit. 
If the axis of the earth were perpendicular to the plane of its orbit 
and if the earth moved forward in its orbit at a uniform speed, the 
differences between the sidereal and solar days would all be the 
same. That is, the solar days would also all be of the same length. 
But the earth's orbit is an ellipse and it moves in such a way that the 
law of areas is fulfilled. When it is near the sun it moves over a 




Tig. 44. The Solar Days Are about 4 Minutes Longer Than the Sidereal 
Days Because the Earth Revolves around the Sun 

greater angular distance in a given time than when it is far from it. 
It follows from this that the solar days are longest — at least so far 
as this factor affects them — when the earth is near the sun. At pre- 
sent the earth is nearest the sun in our winter and farthest from it in 
our summer. Therefore, the solar days measured from noon to noon 
are longer in the winter than they are in the summer of the northern 
hemisphere. 

There is another reason why the solar days vary in length. 
This is because the sun's apparent motion eastward in the sky is 
not along the equator but along the ecliptic. The difference in length 
between the sidereal and solar days depends upon the distance the 
sun moves eastward along the equator. Now, let us suppose for the 
sake of simplicity that the earth's orbit is a circle and that the earth 
moves uniformly along its circumference. In this case the sun will 



104 ' ASTRONOMY 

seem to move uniformly along the ecliptic. But let us assume that 
the ecliptic is inclined to the equator by 23.5 degrees, as is actually 
the case. In Fig. 45, the straight line represents the equator as it 
would be obtained by spreading the celestial sphere out on a plane. 
The ecliptic intersects it at the vernal equinox, V, and at the autumnal 
equinox, A. At V a considerable fraction of the sun's apparent 
motion is northward, and at A southward. Consequently, at these 
points its motion eastward along the equator is less than the average. 
But when the sun is at the summer solstice, S, and at the winter 
solstice, W, its motion is entirely eastward and along the small 
circles, viz, along those declination circles, respectively, 23.5 degrees 
north and south of the equator. At these points it moves eastward 
faster than the average. 

Since the excess in length of the solar day over the sidereal 
depends upon the eastward motion of the sun, it follows that so far 
as the causes now under consideration are concerned the solar days 




Fig. 45. The Sun Moves Eastward Along the Ecliptic Causing 
a Variation in the Lengths of the Solar Days 



are shortest when the sun is at V and A, and longest when the sun 
is at S and W. The sun is at V on March 21, at A on September 
23, at S on June 22, and at W on December 21. So far as this cause 
is concerned, the longest days are in the summer and the winter and 
the shortest in the spring and autumn. 

The actual result is a combination of these two factors which 
influence the length of the solar day. On December 22 the solar 
day is 4 minutes and 26.5 seconds longer than the sidereal day when 
expressed in sidereal time. The solar days then steadily decrease 
until March 26, when the solar day is only three minutes and 38 
seconds longer than the sidereal day. Then they increase in length 
until June 20, which is 4 minutes and 9.5 seconds longer than the 
sidereal day. From June 20 the solar days again decrease in length 
until September 17, which is the shortest day of the whole year, 
and is only 3 minutes and 35.2 seconds longer than the sidereal 



ASTRONOMY 105 

day. They then increase until December 22. The difference in 
length between the longest and shortest day in the year is therefore 
about 51.3 seconds of sidereal time. 

The differences in the lengths of the solar days are not very 
great and it might be supposed that they could be neglected. But 
nowadays the best clocks are made to run so accurately that they 
much more than reveal this difference, and besides the difference 
accumulates. Consequently, it is not practicable to use the solar 
day. This leads to a definition of what is called mean solar time. 
The mean solar day is the average of all the true solar days in the year. 
In sidereal time its length is 24 hours, 3 minutes and 56.556 
seconds It is divided into 24 mean solar hours, an hour into 60 
mean solar minutes, and a minute into 60 mean solar seconds. This 
is the actual day in ordinary use. 

Standard Time. Each meridian on the earth has its own time 
because the sun crosses each meridian at a separate time. Therefore, 
if we were to use mean solar time only those places which are on the 
same meridian would have the same time. It is clear that very great 
confusion would result from this. It was stated above that a degree 
of longitude at latitude 40° is about 53 miles. That is, at our latitude 
there is a difference of four minutes in mean solar time for every 53 
miles, or one minute for every 13 miles. While for many purposes so 
slight a variation as this would not be important, yet in the running 
of trains and boats it would be of the highest importance. This is 
especially true in a country where most of the great trunk lines of 
railways run in an easterly and westerly direction. 

In order to avoid the confusion resulting from each meridian 
having its own time the railways, in 1885, by common agreement, 
adopted the same time for a strip of country between meridians 
about 15 degrees apart. The hour adopted was the correct mean 
solar time for the meridian approximately through the center of the 
strip. Therefore, the error on each side increases to about one-half 
an hour at the extremity of the strip. Since one degree is about 
53 miles in our latitude, the width of these strips averages about 
800 miles. For convenience the strips are not of uniform width and 
do not strictly follow the meridians. It is clear that it would be incon- 
venient for a railway system to change time except at one of the 
divisions of the road. Therefore, the place of the change of time is 



106 



ASTRONOMY 



made to agree with the ends of divisions on the railway. The accom- 
panying map, Fig. 46, shows the time zones in the United States. 
The easternmost division is called eastern time, and has the 
time of the meridian which is 75 degrees west of the Greenwich 
Observatory. This meridian runs through Philadelphia. Next comes 
central time, the mean solar time of the 90th meridian west of Green- 
wich, which runs through St. Louis. Then follows mountain time, 
the time of the 105th meridian, which passes near Denver; and on 
the Pacific Coast they use the mean solar time of the 120th meridian, 
called Pacific time. This meridian passes about 100 miles east of 
San Francisco. 







Fig. 46. The Standard Time Divisions in the United States 



The difference between standard time and mean solar time can 
be calculated when one knows his distance from the fundamental 
time meridian of his zone, because 13 miles corresponds to a difference 
of about one minute. 

If one is east of the fundamental meridian the sun crosses his 
meridian before it does that of the fundamental meridian. Con- 
sequently, by the sun the time is later than it is by standard time. 
That is, he would say that standard time is slow. For example, 
Chicago is about 100 miles east of the meridian through St. Louis, 



ASTRONOMY 107 

and therefore standard time at Chicago is about eight minutes slow. 
West of the meridian standard time is fast. 

Civil and Astronomical Days. The civil day begins at midnight 
and ends at midnight mean solar time. It is clear that it is most 
convenient to have the date change when there are the least activities, 
especially in the business world, and the midnight change satisfies 
these conditions with sufficient accuracy. 

The astronomical day, on the other hand, begins at noon and 
ends at noon, mean solar time. The reason for this is that it is most 
convenient to have the astronomical day change when fewest astro- 
nomical observations are made. About the only ones that can be 
made at noon are those of the sun. 

Place of Change of Date. Suppose one should start at any 
place and go around the earth in a westward direction. On each 
day of his travel the sun would cross his meridian later than if he 
had stayed at home. In making the full circuit he would lose in this 
fashion exactly one day. But if he should go around the earth in 
the other direction the sun would cross his meridian earlier each 
day than if he had stayed at home, and the number of days meas- 
ured by the number of times the sun crossed his meridian would be 
one greater than if he had not made the journey. It is clear from 
this that if one goes around the earth in the westward direction he 
must drop one day from his reckoning in order to be in harmony 
with those who have not made the journey, and if he goes eastward 
he must add one day to preserve harmony. It is convenient to have 
the place of the change of day a fixed one which is well agreed upon. 
It is also obvious that it is convenient to have this where there 
are few inhabitants, for one can see the confusion which would arise 
if on one side of the line through a populous district, as for example 
a large city, people had one day and date and on the other side a 
day and date differing by one day. 

The place where the date is changed is about 180 degrees from 
the meridian of Greenwich. This passes through the Pacific Ocean 
and near very few land areas. There is no meridian in the whole 
earth that would cause less confusion. However, the change is not 
made precisely at the 180th meridian throughout its length. People 
who settled certain islands along this meridian going eastward from 
Europe naturally took their day and date with them, while those 



108 



ASTRONOMY 



going in the other direction also took their day and date. These 
disagreed by one day when they met in the Pacific Ocean. On this 
account there are certain irregularities which are exhibited in Fig. 47. 
The Sidereal Year. Just as there are different kinds of days 
depending upon whether we consider the rotation of the earth with 
respect to the stars or sun, so there are different kinds of years. The 
period of revolution of the earth with respect to the stars is called 
the sidereal year. It is the time required for the sun to pass appar- 
ently from any position among the stars back to the same position 




Fig. 47. The Line at Which Travelers Change Their Day and 

Date, Dropping a Day If Going Westward and Adding 

a Day If Going Eastward 

again. In mean solar time the length of the sidereal year is 365 days, 
6 hours, 9 minutes, and 8.97 seconds, or just a little more than 
365.25 days. 

The Tropical Year. The tropical year is the time it takes the 
earth to move from the vernal equinox around to the vernal equinox 
again. Since the equinoxes have a precession, this year is a little 
shorter than the sidereal year. In mean solar time its actual length 
is 365 days, 5 hours, 45 minutes, and 45.51 seconds. Thus it is 
seen to be about 20 minutes shorter than the sidereal year. In order 



ASTRONOMY 109 

to keep the calendar fixed with respect to the seasons it is necessary 
to use the tropical year. As a matter of fact, this is the year in ordi- 
nary use rather than the sidereal year. 

The Calendar. In very ancient times the calendar was largely 
based on the motions of the moon, which determined the times of 
religious ceremonies. The sun has the same appearance from day 
to day and probably was regarded as somewhat commonplace. The 
moon goes through an interesting and striking change of phases, 
which recur frequently enough so that they are easily remembered, 
and the fact that they systematically repeat was easily discovered. 
It was natural to define time by the phases of the moon, which con- 
tinually vary but constantly recur. 

When, however, records were kept over longer intervals of time 
it was found that the method was not a very convenient one. In 
the first place there is not an integral number of months in the year, 
the number being between twelve and thirteen. Therefore, a cal- 
endar based on the months has the seasons continually shifting with 
respect to it. The calendar of the ancient Egyptians was of this 
character. As the science of astronomy was developed they grad- 
ually turned to a calendar based on the year as a fundamental unit, 
and left the month largely out of consideration. In the year 46 B. c. 
the Roman calendar was reformed by Julius Caesar with the assist- 
ance of the Alexandrian astronomer Sosigenes. This calendar which 
is known as the Julian calendar, was entirely independent of the 
moon, and the year consisted of 365 days, with a leap year every 
fourth year of 366 days. The extra day was added at the end of 
February. This mode of reckoning makes the average year exactly 
365.25 days. It is seen from the result given above that the length 
of the tropical year is about eleven minutes shorter than this. It 
follows from this that the Julian calendar falls one day behind in the 
course of 128 years. By 1582 the calendar was in error more than 
12 days and the matter was getting serious. In that year Pope 
Gregory XIII introduced a slight change. Twelve days were omitted 
from that year and it was agreed that thereafter three leap years 
out of every four centuries should henceforth be omitted. This rule 
again is not quite exact, for the Julian calendar falls behind three 
days in 3 X 128 = 384 years instead of 400 years. Yet the error does 
not amount to a day until after more than 3,000 years have elapsed. 



110 ASTRONOMY 

Although the Gregorian calendar is sufficiently accurate for 3,000 
years, it will some time have to be still further corrected. 

The rule for the leap year is very simple. All years whose 
date numbers are not divisible by 4 are years of 365 days. Those 
years whose date numbers are divisible by 4 are leap years unless 
they are also exactly divisible by 100. Those years whose date 
numbers are divisible by 100 are not leap years unless they are 
exactly divisible by 400, then they are leap years. This is as far 
as the rule has been extended up to the present time. 

While the Gregorian calendar, or at least a slight modification 
of it, keeps the seasons fixed with respect to the year, yet it is in 
many ways imperfect. It is certainly inconvenient to have months 
of different lengths, to have the months in different years begin on 
different days of the week, and to have our numerous holidays and 
festival days, for this reason, continually shifting through the week. 
There are exceptions, of course, in those which are fixed on certain 
days irrespective of the date, as for example Easter and Thanks- 
giving. Recently suggestions have been made for the improve- 
ment of the calendar. 

THE MOON 

The Moon's Apparent Motion among the Stars. The stand- 
ard method of determining the real motions of a heavenly body 
is first to get its apparent motions from the actual observations ; and 
second, to get indirectly its real motions. The moon apparently 
moves eastward among the stars, completing a circuit of the sky in 
a little less than a month. Its apparent orbit is a great circle on the 
celestial sphere, though it does not coincide with the equator. It 
is near the ecliptic, deviating from it by only five degrees, nine min- 
utes. When the moon is in that part of its orbit where the ecliptic 
is north of the equator it crosses the meridian in its diurnal motion 
high in the sky, and when it is at that part of its orbit where the 
ecliptic is south of the equator it crosses the meridian in its diurnal 
motion low in the sky. Since it makes the complete circuit of its 
orbit in a month, there are times each month when it crosses the 
meridian high and others when it crosses it low. When it crosses 
the meridian high it rises in the northeast and sets in the northwest, 
iust as the sun rises in the northeast in the summer time and sets 



ASTRONOMY 111 

in the northwest. When it crosses the meridian at a low altitude 
it rises in the southeast and sets in the southwest, as the sun does 
in the winter time. 

The period of revolution of the moon around the earth can be 
determined by its motion with respect to the stars or its motion 
with respect to the sun. The time it takes the moon to go from a 
certain place among the stars around the sky back to the same place 
again is called the sidereal month. It is found from the observations 
that its length is 27 days, 7 hours, 43 minutes, and 11.55 seconds. 
The time it takes it to go around the sky with respect to the sun is 
called the synodic month. This is clearly longer than the sidereal 
month, for if the moon were at one time in conjunction with the sun 
and certain stars and then moved eastward around the sky back to 
the same stars again, the sun in the meantime (27.3 days) would 
have moved eastward about 27 degrees. The synodic month then 
is longer than the sidereal by the time it takes the moon to move 
over this distance eastward and to overtake the sun. Since the 
moon makes a circuit of the heavens in 27 days, it follows that its 
eastward motion is on the average about 13 degrees a day. Conse- 
quently it will take it a little more than two days to overtake the 
sun after it has arrived back at the same stars again. That is, the 
synodic month is a little more than two days longer than the sidereal 
month. It is found from the observations that the length of the 
sidereal month is 29 days, 12 hours, 44 minutes, and 2.86 seconds. 

The Moon's Phases. The moon shines only by reflected light 
and its phases as seen from the earth depend upon its position rela- 
tive to the earth and sun. Where the sun's rays do not illuminate 
it, it is dark the same as the earth is on its night side. Fig. 48 shows 
the reason of the phases. In this figure the sun's rays come in from 
the right toward the left in sensibly parallel lines. The right side 
of the earth is the day side, and similarly the right side of the moon 
is the day side of the moon. W T hen the moon is at M x the side 
toward the earth is the dark side and the phase is called the new 
moon. The appearance of it is indicated in N x . In about a week 
the moon passes forward in its orbit in the direction indicated by the 
arrow to the point M 2 . At this time half of the illuminated portion 
is visible to the earth and its appearance is indicated in X 2 - This is 
at the first quarter and the moon is at the half-moon phase. In 



112 ASTRONOMY 

another week it moves forward to M 3 , when the illuminated side is 
toward the earth and it appears as N 3 . At the third quarter the 
moon is at M 4 , and has the appearance of iV 4 . 

Let us consider the matter a little more carefully. Suppose the 
earth rotates in the direction indicated by the arrow. Then as the 
observer passes from the day side of the earth to the night side he is 
at at sunset. If he observes the new moon at sunset it will be in 
the same direction as the sun, or in the western sky. At the time of 
half-moon at the first quarter when the sun is in the western sky, 
it is seen from the diagram that the moon is on the observer's merid- 
ian and the light side of it is toward the west. When the moon is 
full the observer sees the sun setting in the west and the full moon 




^5C//Y'S RAYS 



o o 

Fig. 48. The Reason for the Moon's Phases 

rising in the east. Everyone knows that these results are in perfect 
harmony with the facts of observation. 

When the moon is nearly new, that is, when it is between M x 
and M 2 , it presents a thin crescent, convex toward the western sky. 
At this time, however, the rest of it can be dimly seen. It is clear 
from a study of the diagram that the earth has phases as seen from 
the moon similar to those of the moon as seen from the earth, the 
only difference being that they are opposite. That is, when the 
moon is new, as seen from the earth, the earth is full as seen from 
the moon. When the moon is in the position under consideration 
and nearly new the earth as seen from it is nearly full. Conse- 
quently, the moon is to some extent illuminated by the light that 
goes to it from the earth. The darker part of the moon that we 



ASTRONOMY 113 

see faintly when it is at this phase, is illuminated to a slight extent 
by the earth-shine. This earth-shine is about 20 times full moon- 
light. 

Distribution of Sunlight and Moonlight. The amount of light 
received from the moon by the earth is of little importance except 
at the time of full moon. It follows from the preceding section that 
the full moon is exactly opposite the sun in the sky. Consequently, 
when the moon is nearly full it is above the horizon at night while 
the sun is below it, and is below the horizon while the sun is above. 
Because of this fact the light is more equally distributed throughout 
the 24 hours than it would be if they were both on the same side of 
the earth at this phase. This is not only true, but, since the full 
moon is opposite the sun in the sky, when the sun is at the part of 
the ecliptic south of the equator, the full moon is at the part of the 
ecliptic north of the equator. This means that at that time of the 
year, viz, the winter, when we receive the least sunlight, we receive 
the most moonlight, and in the summer when we receive the most 
sunlight, we receive the least moonlight. Everyone has the dim 
impression that the moon shines more brightly in the winter than in 
the summer, and such is a fact, as this discussion shows. Also, in 
the winter the full moon rises far in the northeast and in the summer 
in the southeast. Year after year it is almost exactly the same and 
no changes in the weather conditions can be ascribed to the chang- 
ing relations of the moon relatively to the sun and earth. 

The polar regions of the earth are conceived of as being places 
of perpetual darkness and desolation for six months each year. 
This conception is slightly in error, because after the sun has actually 
set there is a considerable interval in which the twilight is strong 
enough to enable men to carry on all ordinary pursuits. Also, since 
when the sun is below the horizon it is far south, the full moon is corre- 
spondingly north of the equator and is above the horizon. There- 
fore, for half of the dark period the moon between the first and third 
quarters circulates in the sky and lights up the surface of the earth. 
It follows from this that the long night in the polar regions is not 
quite so gloomy as it is often pictured. 

Distance of the Moon. In order to determine the size and 
character of the moon, and also the character of its orbit, it is neces- 
sary to know its distance. The method of finding the distance of 



114 



ASTRONOMY 



the moon is similar to that used by surveyors in finding the distance 
across an impassable gulf or chasm. Suppose the wavy lines in Fig. 
49 represent the banks of an impassabie chasm, and that a surveyor 
wishes to know accurately the distance from B to M. He takes a 
point A on the bank of the chasm which is visible from both B and 
My and then to the left on the bank lays down the lines DA and CB 
in such a way that DC shall be parallel to AB. He then draws a 
line from A to E parallel to BC. He measures the distances AB, 
DE, and EA. Since by construction the triangle AMB is similar 
to DAE, he has the proportion BM : BA = EA : ED, which solved 
gives BM = (BAxEA) -4- ED. It is clear from this that the dis- 
tance across the impassable chasm can be measured as accurately 

as the distances BA, EA, and 
ED are measured on the level 
land. 

As a matter of fact the meas- 
urement can be made a little more 
simply than has been described. 
The method is to set up at B a 
surveyor's instrument, which con- 
sists of a telescope that can be 
turned horizontally and which 
has degrees marked off indicating the direction at which it is 
pointed. After the telescope is accurately adjusted it is pointed at 
M and then turned and pointed at A. The readings of the circle at 
the two different times give the angle MBA. Then the instrument 
is set up at A and pointed at M and then at B. The readings in 
this case give the angle MAB. Now the distance AB is measured. 
Then, in the triangle MBA, the angles A and B and the included 
side are known. It follows from plane geometry that the triangle 
is determined by these three parts. Trigonometry enables one to 
compute the remaining sides when these three are given. There- 
fore, by trigonometry, which is based on such considerations funda- 
mentally as the measurements of D EA described above, the dis- 
tance BM can be computed. 

In Fig. 50, let the circle E represent the earth and suppose A 
is the position of an observer in the northern hemisphere. The line 
AZ points to his zenith. Suppose the moon is on his meridian ; 




Fig. 49. Measurement of the Distance 
across an Impassable Chasm 



ASTRONOMY 115 

therefore, it will be to the south. He has a telescope set up at A 
fixed so that it can move in the plane of the meridian. It is pointed 
up at Z and then turned over until it points to the moon M. The 
readings of a circle similar to that on the surveyor's instrument 
give the angle ZAM. By subtraction the interior angle MAB can be 
found. Suppose there is another observer on the same meridian in 
the southern hemisphere at B. His zenith is in the direction BZ' . 
He sets up a telescope and measures the corresponding angle. Now 
consider the triangle MAB. The angle at A and the angle at B 
are known by the measurements, and since the observer at A knows 
how far he is north of the equator and the one at B how far he is 




Fig. 50. Measurement of the Distance to the Moon by Observations from 
Two Points on the Earth's Surface 

south of the equator, and since the size of the earth is known, the 
straight line AB is also known. Consequently, in the triangle we 
have given two angles and the included side, and the triangle can 
be solved precisely as in the case of the surveyor finding the distance 
across the chasm. This, fundamentally, is the way the distance from 
the earth to the moon is found. It must be understood that in 
carrying out the measurements many artifices are used to secure 
results of the highest order of accuracy. The point insisted on here 
is that the result is in no sense whatever guess-work, but that it is 
based upon careful measurements, and is in reality a measurement 
as much as is the measurement of any distance on the surface of the 
earth. The percentage of error in our knowledge of the distance of 
the moon from the earth is actually much less than the percentage 
of error of any of the ordinary distances we know on the earth. For 
example, it is rarely that the officials of a railway know the length of 
its track between two cities with the same relative degree of accuracy 
that astronomers know the distance from the earth to the moon. 



116 ASTRONOMY 

It is observed that the measurement of the distance from the 
earth to the moon depends upon the measurements of two angles 
and the line joining two places, A and B. Our knowledge of the 
length of this line depends upon knowing the size of the earth. If 
there are any errors in our knowledge of the earth's dimensions they 
introduce corresponding errors in our knowledge of the distance 
from the earth to the moon. If, for some reason, we have obtained 
too large a diameter for the earth then the distance to the moon 
will be too large by the same factor. At the present time so many 
measurements of arcs on the earth have been made that we know 
its size with a very high degree of precision. 

From the methods just explained it has been found that the 
mean distance from the earth to the moon is 238,840 miles. This 
distance is about ten times as far as around the earth. One who has 
traveled over any considerable portion of the earth's surface knows 
how great it is. We can get a mental picture of it by calculating 
how long it would take objects traveling with known speed to go 



©- 



M 



Fig. 51. The Earth and Moon and Their Distance Apart on the Same Scale 

over so great a distance. It is known that sound travels with a high 
velocity. The puff of smoke from a gun is seen and almost imme- 
diately the report is heard. Or, perhaps better, a flash of lightning 
is seen in the sky and in only a few seconds the report of the thunder 
is heard. It is found from observations and experiments that sound 
travels a mile in about five seconds, or at the rate of 720 miles an 
hour. It follows from this and the distance to the moon that, if there 
were an explosion on the moon and the sound of it could come to us, 
it would require 14 of our days and nights to reach us. Of course, 
sound can not come from the moon to the earth because the atmos- 
phere does not extend over that distance. In Fig. 51 the earth and 
distance to the moon are shown to a relative scale and on this figure 
the depth of the atmosphere, supposing it to be 100 miles, would be 
only 6Tro of an inch. 

If a train could come from the moon to the earth running at the 
rate of a mile a minute, night and day, without any stops whatever, it 
would require 166 days for it to come to us. These calculations give a 
better conception than mere figures of the great distance to the moon. 



ASTRONOMY 117 

The Moon's Actual Motion. It follows from the moon's apparent 
motions and its distance that it moves around the earth in an orbit 
whose circumference is about 1,500,680 miles. Dividing this by the 
sidereal period, it is found that the moon's orbital velocity averages 
about 2,290 miles per hour, or 3,357 feet per second. It is found 
from the observations of the apparent diameter of the moon that 
its distance from the earth varies somewhat. Plotting its orbit by 
the method used in determining the shape of the earth's orbit around 
the sun, it is found that the moon's path is also elliptical and that 
the earth is at one of its foci. It does not move uniformly in its 
orbit, but moves in such a way that the radius from the center of 
the earth to it sweeps over areas which are proportional to the time. 

The moon is carried forward with the earth in its motion around 
the sun. The motion of the earth is about 50 times as fast as that of 



.5 



Fig. 52. The Motion of the Moon Relative to the Sun 



the moon in its orbit. Consequently, when the moon is between the 
earth and sun, as at M in Fig. 52, and its motion is backward with 
respect to the earth, it is actually moving forward very fast with 
respect to the sun. The distance from the earth to the moon is about 
tot¥ of the distance from the earth to the sun. It follows from this 
that the motion of the moon toward the sun and away from it, as it 
crosses the earth's orbit, is relatively insignificant compared to its 
motion forward as it is taken with the earth around the sun. The 
consequence of this is that the moon's orbit is concave toward the 
sun at every point and sensibly like that of the earth. 

Up to this point we have spoken as though the earth moved 
around the sun in an elliptical orbit. As a matter of fact, it is the 
center of gravity of the earth and moon which describes this curve, 
these two bodies revolving around their center of gravity in a month. 
This point is only 3,000 miles from the center of the earth, and is 
therefore in round numbers 1,000 miles below its surface. 



118 ASTRONOMY 

The moon always keeps the same face toward the earth. Con- 
sequently it rotates on its axis once while it passes around the earth ; 
that is, its period of rotation is the same as that of its revolution. 
In Fig. 48 the side of the moon which is toward the left when the 
moon is at Mi has turned around so that it is toward the right when 
the moon is at M 3 . 

Size of the Moon. The mean apparent diameter of the moon 
is 31 minutes 8 seconds, the apparent diameter varying by a little 
more than two minutes because of the eccentricity of the moon's 
orbit. When the apparent size of an object is known and its distance 
from the observer is known, it is a simple matter by trigonometry to 
compute its actual size. It turns out that the actual diameter of 
the moon is 2,163 miles. This result is known with the same degree 
of certainty as the distance to the moon. The diameter of the moon 

is about 27 per cent of that 
of the earth, and their rela- 
tive dimensions are shown to 
the same scale in Fig. 53. 





bince the surfaces or sim- 
ilar bodies are as the squares 
of their dimensions the sur- 
face of the moon is about 

Fig. 53. The Ear^n^ Moon Shown on the ^ ft^ Q f ^ earth; ^ 

since their volumes are as 
the cubes of their dimensions the volume of the moon is about ^V 
that of the earth. 

When the moon is on the observer's meridian it is nearer the 
observer than when it is on his horizon by about 4,000 miles. Thus, 
in Fig. 54, is about 4,000 miles nearer M than P is. Therefore, the 
moon ought to look larger when it is near the meridian than when it 
is at the horizon. As a matter of actual fact it is found by measure- 
ment with a telescope that the moon is apparently larger near the 
meridian than when it is on the horizon and the difference is in har- 
mony with these figures. But without an instrument the moon 
certainly appears larger at the horizon. The explanation of this 
peculiar appearance, which is directly opposed to the actual facts, 
is that when the moon is high in the sky there is nothing with which 
to compare its distance, and the observer underestimates greatly 



ASTRONOMY 119 

its distance from us. Our judgment of the size of an object depends 
upon two things, its apparent diameter and our knowledge of its 
distance from us. L" we think it is very close we unconsciously esti- 




Diagram Illustrating Change of Size of Moon 



mate it as being of small size, while if we think of it as being very 
far. away we judge that it is large. It is not difficult to bring a spider 
web near the eye and to force into the consciousness a belief, Urst, 
that it is something very near when it appears very small, as it actually 
is; and second, that it is something very far away when it has the 
appearance of a large cable, instead of a very minute thread. Now 
our estimate of the real size of the moon, or any other celestial 
object, depends in a similar way upon our unconscious estimate of 
its distance. As has been said, for some reason when the moon is 
high in the sky we judge that it is near to us, and consequently it 
appears small. When it is near the horizon it is easy to see that it 
is beyond the buildings and trees which are visible in its direction, 
and that forces into our consciousness the knowledge that it is far 
away. Then unconsciously we picture it as large. The actual 
measurements with instruments prove that the estimate that the 
moon is larger when near the horizon than when high in the sky, is 
purely subjective, and the explanation for this has just been given. 
Mass of the Moon. The mass of the moon relatively to that 
of the earth is determined by the distance of the earth from the 
center of gravitv of the earth and 



Fig. 55. Weighing the Moon 



moon. The principle is the same 

as that of balancing weights on 

the arms of a lever. In Fig. 55 

let W and w represent two weights at distances L and / from the 

fulcrum F. Then by the principle of the lever II" X L = w X I. 

And so in the case of the earth and moon, the mass of the earth Times 



120 ASTRONOMY 

the distance from its center to the center of gravity of the earth and 
the moon equals the mass of the moon times its distance from the 
center of gravity of the earth and moon. The center of gravity of 
the earth and moon being determined from the observations of the 
motion of the earth around the sun, which determine the point 
describing the elliptical orbit, it is possible to find the mass of the 
•moon in terms of the mass of the earth. It turns out that the mass 
of the earth is 81.7 times that of the moon. It follows from the 
volume of the moon given above, and the density of the earth given 
in the description of the earth, that the density of the moon is 3.4 
times that of water. 

The weight of a body on the surface of the earth depends upon 
the mass of the earth and the distance of the surface of the earth 
from its center. In particular, the weight of a body is directly pro- 
portional to the mass of the earth, and inversely proportional to the 
square of its distance from the center of the earth. The correspond- 
ing thing is true on the moon. Using the mass of the moon and the 
size of it given above, it is found that an object on the surface of 
the moon weighs only one-sixth as much as the same object would 
on the surface of the earth. This refers to weighing on a spring bal- 
ance. If the object were weighed with an ordinary balance scale, 
where a small weight is used to balance the body weighed it would, 
of course, weigh the same as on the earth, because the change in 
pull on the body weighed and the balancing weight would be in the 
same ratio. It follows from the fact that a body weighs only one- 
sixth as much on the moon as it would upon the earth, that the same 
force there would throw it six times as high. If a man can jump 
five feet high upon the earth, the same man on the moon, if he could 
live there and exert the same energy, could jump 30 feet high. Vol- 
canic activity on the moon would throw matter six times as high as 
the same activity on the earth. Since matter weighs less on the 
moon, mountains could be piled six times as high before the rock 
would crush and break out at their bottoms. Perhaps this partly 
explains why mountains are so very high and rugged on the moon, 
as we shall presently see. 

Atmosphere of the Moon. The moon has little or no atmosphere. 
This is proved by the fact that its surface always stands out with 
remarkable distinctness, there never being the slightest evidence of 



ASTRONOMY 121 

clouds or obscuring vapor. It is also shown by the fact that when 
the moon passes between us and the sun there is no luminous ring 
around it as there would be if it had an atmosphere. The differ- 
ence is conspicuous when the planet Venus passes between us and 
the sun. This planet has an atmosphere and the illuminated ring 
of its gaseous envelope is visible when it is in a line with the sun. 

One might well ask why the moon has no atmosphere. The 
theory has been suggested that it has been gradually absorbed by 
the rocks of the surface. This is not very probable because while 
the rocks may absorb some atmosphere, on the other hand, they 
also give it forth. As they disintegrate they liberate as a rule large 
quantities of gas. Also there are irregularities on the surface of the 
moon which, if interpreted as indicating volcanic activity in past 
times, means that large volumes of gases have been given forth from 
its interior. 

A better explanation, and one which is almost certainly correct, 
is that the moon has not sufficient gravitative power to hold an 
atmosphere. As was explained above in connection with the atmos- 
phere of the earth and the kinetic theory of gases, there is a tendency 
of the molecules of an atmosphere to escape from the bodies which 
they surround by darting off into space. The gravitative power of 
the moon is so slight that the opportunities for escape are much 
greater than in the case of the earth. Consequently, it is not 
unreasonable to suppose that the atmosphere of the moon, if it ever 
had one, has been lost into space, molecule by molecule. Of course, 
there is no guarantee that at any time in its history it ever had an 
atmosphere comparable to that of the earth. But in view of the 
activities that its surface shows were once taking place there, it 
seems probable that it would now have a greater atmosphere than 
observation shows exists, if it had not been lost in this manner. 

Light and Heat Received by the Earth from the Moon. Direct 
observations of the amount of light and heat received from the 
moon show that at full moon we get about Tnn^Tnnr as much light 
and heat from the moon as from the sun. The average amount of 
light and heat received from the moon compared to that received 
from the sun is very much less than this, probably not more than 
one-fourth as great. Therefore, it follows that we receive more light 
and heat from the sun in 15 seconds than we do from the moon in 



122 ASTRONOMY 

a whole year. The passing of a cloud between the earth's surface 
and the sun for a few minutes reduces the amount of light and heat 
received more than it would be reduced if the moon were taken 
from our sky for a year. 

It follows from these figures that the moon does not have a 
sensible effect in raising the temperature of the earth. It is seen 
from this how absurd it is to suppose that hot spells or cold spells 
depend in any way upon the moon. As a matter of fact, the discus- 
sion of observations covering a very long time do not show any 
certain relation of any kind between the state of the weather and the 
phases of the moon. So far as can be determined from observations 
extending over a century there is no more likelihood of its freezing 
or raining or being hot at one phase of the moon than at another. 

Temperature of the Moon. The average distance of the moon 
from the sun is about as great as that of the earth, and consequently 
if its atmosphere were the same and its rotation were the same its 
climate would be similar to that of the earth. The most important 
difference in this connection between the earth and moon is that the 
moon has no atmosphere. Therefore, the day side of the moon is 
subject to the intense rays of the sun with no protection of clouds 
or atmosphere, and the night side loses its heat rapidly and the 
temperature falls very low. 

It was explained above that the moon keeps the same face 
toward the earth all the time, and consequently that it turns on its 
axis once in a month. Its day is, therefore, a synodic month of 28.5 
of our days. This long period of rotation adds to the extremes of 
temperature which the moon already is shown to have because of 
the absence of an atmosphere surrounding it. For more than 14 
of our days its surface is subject to the burning rays of the sun, 
and then for more than 14 of our days it is in darkness. During the 
long period it receives light and heat from the sun its temperature 
rises very high, probably reaching the boiling point. During the long 
night its temperature falls very low, perhaps 200° or 250° below zero. 
The lowest natural temperature ever known upon the earth, even in 
arctic regions, is about 90 degrees below zero. 

The temperature of the moon can not be found without some 
difficulty. We have instruments which can measure as small amounts 
of heat as the moon sends to us but the difficulty arises in this case 



ASTRONOMY 123 

from the fact that the heat we receive from the moon is partly 
radiated heat and more largely reflected sunlight and heat. It is 
not possible to fully separate the two. If it were, and we had the 
amount of heat the moon radiates to us, we should be able to obtain 
its temperature with a considerable degree of accuracy. The best 
time for doing it and the one in which the reflected light and heat 
do not seriously bother is when the moon passes into the earth's 
shadow. Just before it enters the shadow it has been subject to the 
rays of the sun falling almost perpendicularly upon it. It enters 
the shadow and the sun's light and heat are cut off. (See Fig. 56.) 
The only heat which the observer at receives from the moon at 
this time is that which the moon radiates because its temperature 
has been raised before it entered the shadow of the earth. This heat 
has been measured and from it we have arrived at our ideas concerning 




Fig. 56. The Earth's Shadow and Eclipse of the Moon 

the temperature of the moon. It is an interesting and significant 
fact that, during the two hours required for the moon to pass through 
the earth's shadow, its temperature falls so low that at the end of 
the eclipse we do not receive sensible quantities of heat from it. 

The moon is, therefore, to be thought of as a body whose surface 
is subject to alternating periods of burning and freezing temperatures. 
Clearly, it is impossible for life such as we have upon the earth to 
exist on such a body. There is every reason to believe that it is a 
dead world and probably that it has always been without life of 
any form. 

Surface Conditions on the Moon. The moon appears to be an 
object of light and dark areas as viewed without a telescope. Through 
a telescope the same regions are still apparent, but it is found that 
those which are light are extremely rough while those which are dark 
are relatively smooth. Fig. 57 shows a photograph of the full moon 
in which to some extent the light areas and the dark areas can be made 
out, and can be seen to be, respectively, rough and smooth. 



124 ASTRONOMY 

The most striking feature on the moon is a great number of 
circular pits varying in diameter from a few thousand feet up to 
more than 100 miles. These depressions are called craters. It must 
not be inferred, however, from the name that they are necessarily 
similar, either in their general features or in their origin, to the 




Fig. 57. The Full Moon Photographed at the Yerkes Observatory 

volcanic craters we have upon the earth. They are usually deep 
depressions in the surface of the moon with no evidence of lava flows 
around them, and often, if not generally, with high mountains in 
their interiors. In many cases if their rims were piled into the 
depressions they would not be filled. 

The question of the origin of the lunar craters is not easy to 
answer with any degree of certainty. Arguing from analogy with 
the earth one might suppose they are of volcanic origin. However, 



ASTRONOMY 125 

the peculiarities noted above are against this theory. It seems less 
improbable to suppose that they have been formed by explosions of 
vast accumulations of gas in the interior of the moon. If we suppose 
its temperature was high near the surface, and that in contracting 
large quantities of gas gathered here and there at shallow depths, it 
is not altogether unreasonable to suppose that because of the high 
temperature the gas would occasionally tear its way out through the 
surface with explosive violence. In such an explosion matter would 
be thrown far and wide, depending upon its violence, and much of 
it would fall back into the cavity from which the gas escaped. It 
is not entirely unreasonable to suppose the craters may have origi- 
nated somewhat in this fashion. If they have, the violence of the 
explosion is attested by the long cracks in the rocks radiating from 
the biggest craters and in some cases reaching to a distance of more 
than a thousand miles. They are conspicuously shown around several 
craters in Fig. 57. 

Another hypothesis as to the origin of craters, which has perhaps 
some merit, is that they were formed by the impact of huge meteorites 
striking on the moon from without. In order to form in this manner 
those large craters which are approximately 100 miles in diameter, 
it would be necessary that meteorites very many miles in diameter 
should strike the moon. According to this theory the craters should 
be depressions, as they are seen to be, and there is no reason why the 
matter which constitutes their rims should fill them if it were put 
on the inside. One serious objection to this hypothesis is that the 
craters are all very nearly circular. If they were formed by the impacts 
of meteorites it would be expected that some of them would strike 
the moon glancing blows and make long streaks instead of circular 
pits. If the impact theory is the true explanation of the origin of the 
lunar craters, the heat generated by the impact of the meteorites is 
not a negligible quantity in accounting for their peculiarities. A 
meteorite striking the surface of the moon with the velocity at which 
.meteors enter the earth's atmosphere, would generate enough heat to 
liquefy arid volatilize a considerable fraction of the matter in the 
neighborhood of the point where it struck. This sudden heating of 
the matter in the interior of the crater pits would cause secondary 
explosions and might perhaps elevate the mountains which are found 
in them. 




Fig. 58. The Crater Theophilus 64 Miles Across and 18,000 Feet Deep 




Fig. 59. The Great Crater (Jlavius and Surrounding Region 



128 



ASTRONOMY 



If the craters of the moon had their origin in the impacts of the 
meteorites from the outside the question arises why the earth has 
not been subject to a similar bombardment. These two bodies have 
been associated throughout their evolution as distinct bodies and 
there is no reason assignable why the moon should have been more 
subject to the impact of meteorites than the earth. The reason 



iMMBi 



& 





Fig. 60. The Lunar Apennines, Named by Galileo Who First Saw Them 

for the absence of such evidence on the earth is that the earth 
has an atmosphere surrounding it and is nearly covered with 
water. These elements disintegrate the rocks, and in the course of 
the millions of years which have elapsed since such a bombardment, 
has taken place, if indeed it ever did take place, the evidences of 
these impacts have been totally destroyed. On the other hand, on 



ASTRONOMY 129 

the moon there is no atmosphere and no water and the rocks would 
be preserved as they were originally formed. The chief disintegrating 
effects are the extremes of temperature which have been described 
above. 

One of the most interesting craters is Theophilus, a photograph 
of which is shown in Fig. 58. This crater is 64 miles across. Its 
depth is from 16,000 to 19,000 feet. This result is obtained by meas- 
urements of the length of the shadows in its interior, knowing the 
altitude of the sun as seen from the moon when the photograph was 
taken. It is simply the problem of determining the height of a building 
from the length of its shadow when the altitude of the sun is known. 
In the interior of Theophilus there are mountains which are about 
16,000 feet high. In the photograph their shadows can be seen 
stretching off to the left, long, sharp, and spire-like. They show the 
rugged character of these mountains. They stand up from the floor 
of the crater higher than any mountains on the earth reach above the 
plateaus on which they rest. 

There are many places on the moon where a number of genera- 
tions of craters can be seen. In Fig. 59 it is possible to see large old 
craters and new ones formed on their remains and in their interiors. 

The moon has a number of mountain ranges and very many 
isolated peaks. One of the most remarkable ranges is the Apennines, 
Fig. 60, named by Galileo after the Apennines of Italy. These 
mountains are extremely rugged and very high, many of their peaks 
towering more than 20,000 feet above the plateaus on which they stand. 

Fig. 61 shows a photograph of one of the dark, relatively smooth 
places called by Galileo Mare Serenitatis, or the Serene Sea. With his 
little telescope he was not able to discern the craters which we see 
in it and the ranges of hills which are running across it. Since we 
have mountains on the earth and also on the moon, he came to the 
conclusion that these two objects were very similar. Therefore, 
it was natural for him to suppose that there were seas on the moon 
as well as on the earth, and these smooth places were the only things 
which could be interpreted as being vast bodies of water. It is now 
clear that there is no water there whatever, and there is no evidence 
that there ever has been any. In all probability the side of the moon 
which we never see is in all essential respects similar to that which 
is toward the earth. 



ASTRONOMY 131 

Besides the craters, the mountains, and the plains of the moon, 
there are a number of remarkable long, narrow, and deep cracks in 
its surface called rills. In some respects they resemble the Grand 
Canon of the Colorado more than anything else on the earth. But 
the Grand Cafion of the Colorado was made by the river cutting 
its way through the rock; while the rills on the moon have certainly 
had a different origin. They may be simply cracks in the rock of 
the shrinking mass. If the cracks were made on the moon by the 
breaking rocks it was certainly shaken by severe earthquakes, for 
it is well known that earthquakes here on the earth are usually, if 
not always, produced by the breaking of the rocks of the earth's 
crust and their slipping on each other. For example, the destruc- 
tive earthquake in San Francisco in 1906 was due to a crack nearly 
parallel to the coast several hundred miles in length, and the slip- 
ping of the rock on one side of the crack past that on the other side. 

Eclipses of the Moon. When the moon passes into the earth's 
shadow it is eclipsed. It might be imagined from Fig. 48 that the 



^ tfog rft QRBrr 




Fig. 62. The Moon Is Not Eclipsed Every Month Because Its Orbit 
Is Inclined to the Ecliptic 

moon would be eclipsed every time it is full. The reason it is not 
is because the plane of its orbit is inclined to the ecliptic about five 
degrees. Since the sun apparently travels on the ecliptic the shadow 
of the earth travels along the ecliptic. In Fig. 62 let the straight 
line represent the ecliptic and the curve the moon's orbit. Let the 
circle S represent the cross section of the shadow of the earth at the 
distance of the moon. Let M represent the moon. The point A 
is the place where the moon's orbit crosses the ecliptic from south 
to north, and is called the ascending node, while D, the other place 
where the moon's orbit crosses the ecliptic, is called the descending 
node. If the moon passes the earth's shadow when it is near .1 and 
D, clearly it will pass through the shadow and be eclipsed. If it 
passes the shadow when it is between A and D and not when near 
one of these points, it will miss the earth's shadow and will not be 
eclipsed. 



132 ASTRONOMY 

The moon travels around the earth about 13 times in a year 
and consequently passes the earth's shadow about 13 times in a 
year. At two of these times it passes the shadow near the points 
A and D, and at these times the moon is eclipsed. The other eleven 
times the shadow of the earth is so far from A and D that the moon 
does not pass through it. It is easy to see, therefore, why the moon 
is not eclipsed every month, and why it is eclipsed twice a year on 
dates which are six months apart. 

The points A and D are not fixed on the ecliptic. The attrac- 
tion of the sun for the moon disturbs its orbit and causes the points 
A and D to move backward along the ecliptic. For this reason the 
eclipse at A occurs earlier each succeeding year; and similarly at 
D. The points A and D make a revolution in about 19 years. 
Consequently, the time of eclipses shifts throughout the whole year 
in a period of 19 years. 

The chief scientific uses of an eclipse of the moon are to deter- 
mine its temperature, as described above, and to search for its possi- 
ble satellites. When the moon is new it is in the direction of the sun 
and faint objects can not be seen in its vicinity. When it is full it 
gives so much light that faint objects can not be seen near it. But 
when it is eclipsed its light is diminished to such an extent that if 
there were any small satellites revolving about it we should have a 
good chance of photographing them. Up to the present time no 
satellites of the moon have been discovered and there is no particular 
reason for believing they exist. 

Eclipses of the Sun. If the orbit of the moon were exactly in 
the plane of the ecliptic, the sun would be eclipsed at every new 
moon. But the inclination of the moon's orbit causes this phenom- 
enon to be relatively rare. In Fig. 62 we may think of S as repre- 
senting the sun itself instead of the earth's shadow. The moon 
passes the sun 13 times a year, but passes between the earth and the 
sun only when the passage is made near A or D. Therefore, the 
eclipses of the sun occur only twice in the year, six months apart. 
This statement requires a slight correction because, if the sun is 
eclipsed when it is to the left of A, it is possible under certain circum- 
stances for the moon to make a revolution of the sky and partially 
to eclipse it again when it is to the right of A and still near to it. 
The circumstances are similar relative to the point D. It is possible, 



ASTRONOMY 133 

therefore, to have four eclipses of the sun in a year. Hence, taking 
the lunar and solar eclipses together it is possible to have six in a 
year, two of the moon and four of the sun. 

Relative Number of Eclipses of Sun and Moon as Observed 
from Any One Place. In Fig. 63, suppose S represents the sun, E 
the earth, and M 1 the moon at the time it is eclipsed. This eclipse 
can be seen from the half of the earth on the side toward it. Since 
it takes the moon about two hours to pass through the earth's shadow, 
the eclipse is visible not only to half the earth, but also to the part 
which is rotated into view of it during the two hours. Since there 
are two eclipses of the moon a year and each one is visible to at least 
half the earth, it follows that on the average at every place on the 
earth one eclipse of the moon per year is visible. 

Let M 2 represent the position of the moon when the sun is 
eclipsed. The sun will be eclipsed only within the part of the shadow 




Fig. 63. Diagram for Explaining the Reason of Eclipses of the Moon and Sun 

cone from the moon which strikes the earth, i. e., at the region P. 
The moon, passing around the earth, causes this shadow to strike 
across the earth in a path whose width is generally less- than 100 
miles, and whose length is a few thousand miles. 

Fig. 64 shows the path of a total eclipse of the sun as given in 
the nautical almanac. It is seen from this how small a portion of 
the surface of the earth is totally shadowed during an eclipse. It 
follows that in spite of the fact that there are more eclipses of the 
sun than of the moon, the number observed at any one place is very 
much less. Everyone who has paid any attention to celestial phe- 
nomena has seen an eclipse of the moon, but comparatively few 
people have seen a total eclipse of the sun. While the path of totality 
is very narrow, there is a large region from which the sun is seen as 
partially eclipsed. A partial eclipse is relatively of small interest 
as compared with a total eclipse. 



134 



ASTRONOMY 



Fig. 65 shows the paths of total eclipses of the sun from 1894 
to 1973. It is seen from this map that there are large regions of 
the earth from which a total eclipse is not visible, and in fact that 
only a small part of the whole earth is eclipsed at all, during the 80 
years which it covers. The fact that total eclipses of the sun are 
startling and not very frequent led the ancients carefully to record 
them. Their records have thus been of assistance to historians 
in some cases in fixing the dates in ancient chronology. If an 



LOTtG/TVPE WEST S^ GREENW/CH 

°S °£ °S °§ I *% °S °s> 



LOMG/TUDE EAST Y G.IEErtW/Cti 



^ 



%*%» n?-^:^^i 




Fig. 64. Path of a Total Eclipse of the Sun 

ancient chronicler described an eclipse at a certain place and stated 
the date of it in his system of counting time, it is possible to locate 
that date in our system of counting time, because the astronomers 
computing back across the centuries can tell the historians at what 
time an eclipse in that part of the world could have occurred. 

One of the uses of the eclipses of the sun is the determination 
of the period of the moon around the earth. It is clear that at the 
time of an eclipse the moon is exactly between the earth and the sun. 
At some later time it is again between the earth and the sun and 
there is another eclipse. If the whole interval and the number of 
revolutions the moon has made in the meantime are known, it is 



ASTRONOMY 



135 



possible to find the period of one revolution by dividing the whold 
time by the number of revolutions. The advantage in this methoe 
lies in the fact that eclipses have been observed for a very long time 
and the errors of observations are divided up because of the very 
many revolutions the moon has made in the meantime. 

A second use of eclipses of the sun is the study of the atmosphere 
and corona of the sun. The corona is visible only at the time of 
total eclipses and is therefore subject to study only during the few 
minutes of eclipses which occur at rare intervals. 

A third use of solar eclipses is that during the periods of totality 




Fig. 65. Paths of Total Eclipses of the Sun 

a search can be made for possible planets revolving so close to the 
sun that they are not visible unless its bright rays are screened off. 
A screen in the atmosphere covering it is of no use, for the illuminated 
atmosphere around is brighter than such objects would be. But the 
distant moon is beyond our atmosphere and when it eclipses the sun 
it makes the sky dark, allowing the region near the sun to be 
searched, particularly by photography, for undiscovered planets. 
So far none have been discovered, and now so many photographs 
have been secured during eclipses that it is improbable that any with 
a diameter exceeding 100 miles exists in close vicinity of the sun. 



Vl'VJ 



\ I : 







WM 



THE MOON'S DISK 
The view shows the disk at 9f days, photographed with 40-inch refractor j 



ASTRONOMY 

PART III 



THE SOLAR SYSTEM 

Members of the Solar System. The members of the solar 
system are the sun, the planets, and their satellites, the planetoids, 
the comets, and the meteors, though it may be that many of the 
comets and meteors are only temporary members of the solar family. 
The sun is in all respects the most important body in the system. 
Its gravitative power holds the planets in their orbits, and its light 
and heat illuminate and warm them. It is impossible to consider 
the planets and comets without considering their relations to the 
sun, but it is quite possible to discuss the sun without particular 
reference to the planets. For the present we shall be interested in all 
those members of the system except the sun. 

There are eight planets in the solar system, which in the order 
of their distances from the sun are Mercury, Venus, Earth, Mars, 
Jupiter, Saturn, Uranus, and Neptune. The first six have been 
known from prehistoric times. Uranus was discovered by Sir Wil- 
liam Herschel in 1781, and Neptune was discovered by Galle in 1846. 

The planetoids are like the planets, whence their name, except 
that they are very small and very numerous. Nearly all of them 
revolve around the sun in the region between the orbit of Mars and 
the orbit of Jupiter. The comets and meteors are wandering mem- 
bers of the system which pass around the sun in elongated orbits, 
sometimes going out so far they probably never return. 

It is possible to find the distances of the planets in terms of the 
earth's distance by rather simple observations. In Fig. 66, let S 
represent the sun, E the earth, and V Venus. Suppose Venus is at 
its greatest apparent distance from the sun as seen from the earth. 
Then the angle at V is a right angle. The angle a is given by the 



138 



ASTRONOMY 




Fig. 66. Finding; the Relative Distance of 

Venus from Observations at the Time 

of Its Greatest Elongation 



observations. The angle at S is therefore known, since the sum of 
the interior angles of a triangle equals two right angles. Conse- 
quently, in the triangle ESV the angle at E and the angle at S are 

known and the included side ES 
is the distance from the earth to 
the sun. From this the distance 
SV can be computed. The prob- 
lem is a little more difficult for 
planets which are farther from 
the sun than the earth is, but it 
is solved in essentially the same 
way. 

Orbits of the Planets. The 
character of the orbits of the 
planets was first found by Kepler 
about 1618 by discussing partic- 
ularly Tycho Brahe's observations 
of Mars. The three laws of planetary motion which he discovered are : 
Law I. Every planet moves so that the radius from the sun to it 
sweeps over equal areas in equal intervals of time, whatever their length. 
Law II. The orbit of every planet is an ellipse ivith the sun at 
one of its foci. 

Law III. The squares of the periods of any two planets are to 
each other as the cubes of their respective mean distances from the sun. 
To these laws, which relate to the fundamental properties 
of the motions of the planets, it might be added that the planes of 
the orbits of the planets are nearly coincident and that the planets 
all revolve around the sun in the same direction. It is also an impor- 
tant fact that the eccentricities of their orbits are in all cases small. 

From Kepler's laws of motion Newton deduced most important 
consequences. He proved, in 1686, that it follows from the first law 
of motion that the forces to which the planets are subject are directed 
toward the sun. Before this time there was no well-established 
connection between the sun and the motions of the planets. In fact, 
it was generally supposed that there was some force continually 
urging the planets on in their orbits. As a preliminary to this con- 
clusion Newton laid down the fundamental laws of motion given 
above in connection with the motions of the earth. 




ASTRONOMY 139 

Newton also showed that it follows from Law II that the forces 
to which the planets are subject vary inversely as the squares of 
their distances from the sun. He proved in this connection that if 
this is the law of force the elliptical orbits are not the only ones 
possible. It is equally possible for a body to move subject to the 
law of gravitation in a parabola or a hyperbola. These curves are 
similar in many respects to the ellipse. 

In Fig. 67 let S represent the sun and E an ellipse with one of 
its foci at S. If the point A on the ellipse is kept fixed and the one 
focus remains at S, and if the other end of 
the ellipse is moved away to the right to 
infinity, then the ellipse becomes the curve 
P, which is a parabola. A parabola has but 
one focus. The two arms of the parabola are 
more nearly parallel as the distance to the 
right increases, and approach exact parallelism 
as the distance to the right approaches infinity. Fig - 67 eta r^ or (>bits Plan " 
If the arms of the parabola are opened out so 
that they are no longer ultimately parallel, we get the hyperbola H. 

Some of the comets move in parabolas and possibly a few in 
hyperbolic orbits. It follows that they also move around the sun 
in obedience to the law of gravitation. 

It follows from Kepler's third law that if all the planets were 
at the same distance from the sun they would be attracted by it 
the same per unit mass. This result is by no means self-evident. 
For example, the sun might attract different kinds of matter differ- 
ently; and if so it would attract the planets differently if they were 
all at the same distance unless they were made of precisely the same 
materials in the same proportions. Since it is improbable that their 
different substances are in exactly the same proportion, it is improb- 
able that, if gravitation were selective, they would all be attracted by 
the same amount if they were at the same distance. 

Law of Gravitation. The law of gravitation is one of the greatest 
and most far-reaching discoveries ever made in science. Stated in 
its generality it is this: 

Every particle of matter in the universe attracts every other par- 
ticle with a force which is proportional to the product of their masses 
and which varies inversely as the squares of their distances apart. 



140 ASTRONOMY 

It relates every particle in the universe to every other par- 
ticle. If the position of any mass in the whole universe changes, 
the force which it exerts on every other particle in the universe is 
changed because, according to the law, force depends upon the 
distance. If a person moves, the gravitative force reaching out 
from him to the two farthest bodies is changed. If, as is now 
believed, every mental activity is accompanied by a physical change 
in the brain, then every thought is accompanied by a change of 
gravitative force throughout the universe. Of course, these changes 
are exceedingly minute and may be for all practical purposes entirely 
neglected. The point of interest here is the fact of their existence. 

More immediate and important consequences of the law of 
gravitation are the motions of the heavenly bodies and their influences 
upon one another. After the law was once discovered it became an 
instrument for further discoveries. Time after time mathematicians 
have predicted, on the basis of the law of gravitation, things which 
ought to be observed and have told the observers when and where 
to look for them. The exactness of the law of gravitation is shown 
by the fact that their predictions have always been verified. No 
other law in all the realm of science is subject to such delicate tests 
and is proved with so high a degree of certainty. It is for this reason 
that it is used with such confidence in arriving at results which can 
never be reached by direct processes. For example, in the study of 
the interior of the earth it was inferred from the nature of the changes 
produced in the rotation of the earth by the attraction of the moon 
and sun on its equatorial bulge, that its interior is on an average very 
rigid. This result is no more certain than the laws and the obser- 
vations upon which it is based. The observations are subject in this 
;case to no serious error, and our confidence in the conclusion is great 
because of its being based upon the fundamental law of gravitation. 

The law of gravitation was the most important discovery of 
Sir Isaac Newton, one of the greatest men the world has produced. 
In Westminster Abbey where England buries the members of its 
royal family and the great men it has produced, there is a tablet 
erected in honor of the memory of Newton on which is an inscription 
in Latin which translated reads: "Mortals, congratulate yourselves 
that so great a man has lived for the honor of the human race." 
This splendid tribute scarcely surpasses those expressions of esteem 



ASTRONOMY 141 

made by the foremost scholars of the world who have worked in the 
same line. The brilliant German, Leibnitz, who was a contemporary 
and in some respects a rival of Newton, said: "Taking mathematics 
from the beginning of the world to the time when Newton lived, 
what he had done was much the better half." The French mathe- 
matician, LaGrange, who was one of the greatest masters of celestial 
mechanics, said: "Newton was the greatest genius that ever existed, 
and the most fortunate, for we cannot find more than once a system 
of the world." The English scientist, Whewell, wrote in his "History 
of Inductive Science": "It (the law of gravitation) is indisputably 
and incomparably the greatest scientific discovery ever made 
whether we look at the advance which it involved, or the extent of 
the truth disclosed, or the fundamental and satisfactory nature of 
this truth." 

Newton, with the humility characteristic of great minds who 
see how little they know compared with that which they do not 
know but would like to understand, said: "I do not know what I 
may appear to the world; but to myself I seem to have been only 
like a boy playing on the seashore and diverting myself in now 
and then finding a smoother pebble or a prettier shell than the ordi- 
nary, whilst the great ocean of truth lay undiscovered before me." 

One of the satisfactory things in science is that in it are dis- 
covered fundamental laws such as the law of gravitation. It satisfies 
our instincts for absolute truth. 

Distances of the Planets. The mean distances of the planets 
from the sun, which means half of the lengths of their orbits, are : 

Mercury 36,000,000 miles 

Venus 67,200,000 miles 

Earth. . 92,900,000 miles 

Mars , 141,500,000 miles 

Jupiter 483,300,000 miles 

Saturn 886,000,000 miles 

Uranus 1,781,900,000 miles 

Neptune 2,791,600,000 miles 

The diameter of the sun is about 866,000 miles. 

The figures which have been given represent so vast distances, 
and cover so wide a range, that it is difficult to form any adequate 
mental picture from them. The relative dimensions of the system 
can be shown better by means of a diagram than by the numbers. 



142 



ASTRONOMY 



Suppose, for example, we should draw a map of the system, taking 
for the orbit of Mercury a circle one inch in diameter. On this scale 
the sun would be represented by a circle -fa of an inch in diameter, 
and the earth by an invisible dot, scarcely more than Wto of an inch 
across. On the same scale the distance from the sun to Neptune 
would be a little over three feet. Consequently, it is not possible to 
put such a picture on the printed page. If we should represent the 
orbit of Neptune by a circle four inches in diameter, which is about 
as large as can be put on the page, the orbit of Mercury would be 
about -20 of an inch in diameter. Obviously, then, it is impossible on 
the printed page to give a diagram showing the whole system to 
scale. However, this should not deter the reader from making such 

a diagram on a suitable place as, 
for example, on a blackboard or 
a very large sheet of paper. 

Certain features of the system 
can, however, be brought out by 
means of the diagrams. Fig. 68 
shows the orbits of the four plan- 
ets nearest the sun to relative 
scale. It is apparent from the 
figure that they are spaced with 
a considerable degree of regu- 
larity. 

Fig. 69 shows the orbits of the 
planets beginning with Mars and 
ending with Neptune. Now it is possible to imagine the orbits of the 
three planets which are nearer the sun than Mars inside the small 
circle which represents its orbit. From this diagram it is evident 
that the farthest planets are spread out at enormous distances. 
The space between the orbits of Jupiter and Saturn is much greater 
than all that interior to the orbit of Jupiter; and that between the 
orbits of Saturn and Uranus is greater than all of that interior to the 
orbit of Saturn; and similarly for the orbits of Uranus and Neptune. 
The apparent diameters of the sun, as seen from the different 
planets, are inversely as their distances from the sun. The sun as 
seen from the earth has an apparent diameter of a little over half 
a degree. As seen from Mercury its apparent diameter is nearly 




Fig. 68. The Orbits of the Terrestrial 
Planets to the Same Scale 



ASTRONOMY 143 

three times this. Its apparent area, which varies as the square of 
its apparent diameter, is consequently nearly nine times as great as 
seen from Mercury as it is as seen from the earth. Considering the 
other extreme we find, since Neptune is 30 times as far from the sun 
as the earth is, that the apparent diameter of the sun as seen from 
Neptune is only one minute of arc. Now, a body whose apparent 

ORBIT OF qCPTV/w 




Fig. 69. The Orbits of the Major Planets to the Same Scale 

diameter is less than one minute appears to the unaided eye like a 
point of light. Therefore, as seen from Neptune, the sun would 
appear like a star, only immensely brighter than any star in our sky. 
Its apparent area as seen from Neptune would be wo that as seen 
from the earth. Consequently, the amount of light and heat received 
on Neptune per unit area is 900 that received by the earth. One 
is apt to draw the erroneous conclusion that Neptune is a rather dark 
place. But when we reflect that moonlight is equal to only grnrNnro 



144 



ASTRONOMY 



TABLE IV 
Planets in Order from Sun with Apparent and Actual Diameters 



PI 


Greatest Apparent Diameter 


Diameter 




(seconds of arc) 


(miles) 


Mercury 


13. 


2,765 


Venus 


67. 


7,826 


Earth 




7,913 


I 
Mars 


25. 


( 4,352 (equatorial) 
I 4,312 (polar) 


Jupiter 


50. 


f 90. 190 (equatorial) 
184,570 (polar) 


Saturn 


20. 


f76,470 (equatorial) 
169,780 (polar) 


Uranus 


49. 


34,900 


Neptune 


21. 


32,900 



of sunlight, while the illumination of Neptune is only 9-5-0 that of 
the earth, it is seen that sunlight on Neptune is really an intense 
illumination, being about 700 times full moonlight here on the earth. 

The climate of a planet depends to a large extent upon the 
amount of light and heat it receives from the sun. Other things being 
equal, particularly the constitution of the atmosphere and the radia- 
tion, the climate of Mercury would be the hottest of all the planets, 
and that of Neptune the coldest. Since Neptune receives so small an 
amount of heat and light compared to the earth, it is clear that unless 
its atmosphere is peculiarly adapted to preserving a high temperature 
or unless the planet is still hot itself, its surface must be very frigid. 

Dimensions and Masses of Planets. The diameters of the plan- 
ets differ almost as much as their distances from the sun. In a 
general way those which are near the sun are small, and those which 
are far away are large. Their actual sizes are found from measure- 
ments of their apparent diameters after their distances are known. 
Table IV, based on measurements by Barnard at the Lick Observa- 
tory, gives the planets in their order from the sun, in the second 
column their greatest apparent diameters as seen from the earth, 
and in the third column their actual diameters in miles. 

The circles of Fig. 70 show better than these numbers the rela- 
tive dimensions of the planets. The striking thing is the smallness 
of the earth with respect to the great planets. 

Since the surfaces of similar bodies are as the squares of their 
like dimensions and the volumes as the cubes of their like dimen- 



ASTRONOMY 



145 



TABLB V 
Surface and Volume of Planets as Compared to Earth 



Planet 


Surface 


Volume 


Planet 


Surface 


Volume 


Mercury 
Venus 
Earth 
Mars 


0.12 
0.98 
1.00 
0.30 


0.04 
0.97 
1.00 
0.16 


Jupiter 
Saturn 
Uranus 
Neptune 


122.0 
85.6 
19.5 
17.3 


1,350.0 
790.0 

85.8 
71.9 



sions, it follows that the differences in surfaces and volumes of the 
planets are much greater than the differences in their diameters. 

Table V gives the comparison taking the surface and volume 
of the earth as a unit. 

JUPITER 



o 

MERCURY 




O 

VEHUS 

O 



o 

MARS 



The Planets Drawn to the Same Scale 



The masses of the planets depend upon their size and upon their 
density. The masses of those that have satellites are found by the 
time it takes their satellites to revolve around them. It is easy to 
see that the greater the mass of planet the shorter will be the period 
of the satellite at a given distance. The formula relating their period, 
the distance, and the mass of the planet, is one which is derived 
from the law of gravitation and is given in celestial mechanics. It is 

27tai 



P = 



kV'.M + 



m 



146 



ASTRONOMY 



TABLE VI 
Masses and Densities of Sun and Planets 



Object 


Mass (Earth =1) 


Mass (Sun= 1) 


Density (Water = 1) 


Sun 


332,000.0 


1 


1.41 


Mercury 


0.033 


l 
F6 4fOT5TT 


3.70 


Venus 


0.82 


TOToZO 


4.89 


Earth 


1.0 


iWtfou 


5.53 


Mars 


0.11 


sflsowir 


3.95 


Jupiter 


317.7 


ToW 


1.53 


Saturn 


94.8 


350^ 


0.72 


Uranus 


14.6 


"£2700 


1.22 


Neptune 


17.0 


, 1 


1.11 


T9500 



where P is the period expressed in days, a the distance from the 
satellite to the planet expressed in terms of the earth's distance from 
the, sun, k a constant which equals about -gV, M the mass of the 
planet, and m the mass of the satellite. 

The masses of those planets which do not have satellites are 
found from their attractions for one another, and for comets which 
pass near them. The planets are so far apart and they are so small 
compared to the sun that their mutual attractions are not large 
enough to enable us to determine their masses very accurately. 
When comets pass near them more exact results can be secured, but . 
the best that can be obtained in this way is very much less accurate 
than those furnished by the periods of the satellites. 

Since the diameters of most of the planets are known and their 
masses are found as has just been explained, it is possible to determine 
their densities by dividing the masses by the volumes. Table VI 
gives the results for the sun and the planets. In the second column 
the mass of the earth is taken as the unit, and the masses of the 
other members of the system are expressed in terms of it. In the 
third column the mass of the sun is taken as the unit; and in the 
fourth column the densities of all these bodies are given, taking 
water as the standard. 

It is seen from Table VI that Jupiter is not only much larger 
than any other planet, but its mass is more than three times that of 
any other planet and about two and a half times that of all the other 
planets combined. It is also observed that the earth is the densest 



ASTRONOMY 



147 



TABLE VII 
Comparative Surface Gravity of Sun and Planets 



Object 


Surface Gravity 


Object 


Surface Gravity 


Sun 


27.7 


Jupiter 


2.61 


Mercury 


0.38 


Saturn 


1.19 


Venus 


0.86 


Uranus 


0.88 


Earth 


1.00 


Neptune 


0.88 


Mars 


0.38 







member of the solar system. The rarest one is the planet Saturn, 
whose mean density is about three-fourths that of water. 

The surface gravity, or the relative weight of an object on the 
surface of a planet, depends upon its mass and dimensions. Accord- 
ing to the law of gravitation the weight, which is a consequence of 
the attraction, is directly proportional to the mass of the planet and 
inversely proportional to the square of the distance from its surface 
to its center. From this law and the preceding tables Table VII 
has been computed . 

It is seen from Table VII that although the earth has a greater 
density than any other member of the system, its surface gravity is con- 
siderably less than that of Jupiter and the sun. In the case of Saturn 
its larger mass is almost exactly 
offset by its greater diameter. 

Periods of the Planets. The 
periods of the planets depend 
upon their distances from the 
sun, the greater the distances the 
longer the period. In fact, the 
formula for determining the peri- 
ods is given in the preceding 
article, where M in the present 
case must be taken to represent 
the mass of the sun and m the 
mass of the planet. The period 
referred to in the present connection is the time it takes a planet 
to revolve around the sun as observed from the sun. This is called 
the sidereal period. There is another period which is more im- 
portant for observational purposes known as the synodic period. 




Fig. 71. Definition of the Synodic Period 



148 



ASTRONOMY 



In Fig. 71, let S represent the sun, and the two circles the orbits 
of Venus and the earth, respectively. Suppose at a certain time the 
sun, Venus, and the earth are in a straight line at Sl^E^ Suppose 
the directions of motion are indicated by the arrows in the diagram. 
Venus moves faster than the earth both in miles per second and in 
angle; consequently, the line from S to V will move on ahead of the 
line from S to E, and after a time will gain a revolution on it. Let 
us suppose that by the time the earth gets around to E 2 Venus will 
have gone around its orbit back to V lt and on the second time around 
up to V 2 , so that it is again in a line with the earth. It will be seen 
by an examination of the diagram that, under the hypotheses, the 




The Planet Mars in Opposition 



earth, Venus, and the sun have not been in a straight line since they 
were at Sl^E^ This period from a certain relative position to the 
same relative position again is called the synodic period. 

Instead of supposing that the earth, Venus, and the sun are 
initially in a straight line, we might start from the time Venus seems 
to be farthest from the sun, as indicated in Fig. 72, with the earth at 
E x and Venus at V v In this case when the earth gets to E 2 , Venus 
will be at V 2 and will again be at its apparent greatest distance from 
the sun. This is also a synodic period and exactly equal to the pre- 
ceding. When the earth, Venus, and the sun are located relatively 
to each other, as indicated in Fig. 72, Venus is in the position best 
observable from the earth. If the planet were farther from the sun 
than the earth is, the straight line situation, indicated in Fig. 71, 
would be the time when observations could be most advantageously 



ASTRONOMY 149 

made. When the relations are as indicated in Fig. 72, the planet is 
said to be in greatest elongation. That is, as it is observed from the 
earth it is farthest out from the sun. When the situation is as 
indicated in Fig. 71, the planet is said to be in conjunction with the 
sun. In Fig. 73, which shows the orbit of the earth and Mars, the 
planet is said to be in opposition when the relations of the bodies are 
as indicated in the diagram. In observing a planet which is farther 
from the sun than the earth, obviously the most convenient time 
for observations is when it is in opposition, for then it is nearest to 
the earth and the illuminated side is toward the earth 

It is obvious from Fig. 72 that a planet which is nearer the sun 
than the earth, can have an elongation either side of the sun. If the 
planet is to be observed in the evening, which means that it must be 
above the horizon after the sun 
has set, it must be east of the 
sun. Since the evening is in gen- 
eral a more convenient time for 
observation than the early morn- 
ing, we shall make our calcula- 
tions for the eastward elongation. 
Since the earth rotates in the 
same direction that it goes around 
the sun, viz, from west to east, 
it follows that Venus has a west- 
ward elongation when its rela- Fig 74 The M otto7s of Venus Eastward 

tions to the sun and the earth and Westward Past the SuQ 

are as indicated in Fig. 72. This can be seen by following a point 
on the earth in its daily rotation. The point will pass under Venus, 
i. e., Venus will apparently cross its meridian, before it passes under 
the sun, and consequently Venus will set before the sun does. 

Suppose Venus has its greatest eastward elongation and consider 
Fig. 74. When Venus is in the position V 2 , it has its greatest eastern 
elongation. Suppose for simplicity that the earth stands still while 
Venus moves forward in its orbit. It will pass between the earth and 
the sun and arrive at its greatest westward elongation at V v Then 
it passes apparently back across the sun on the side of the sun oppo- 
site to the earth and arrives again at V 2 . It is clear from the dia- 
gram that the time from V 2 to V ly i. e., from eastward elongation to 




150 



ASTRONOMY 



TABLE VIII 
Data from Which to Compute Times Favorable for Observation of Planets 



Planet 


Sidereal Period 
(Years) 


Synodical Period 
(Years) 


Date of Eastern Elon- 
gation or of Opposition 


Mercury 

Venus 

Earth 

Mars 

Jupiter 

Saturn 

Uranus 

Neptune 


24 

0.62 

1.00 

1.88 

11.86 

29.46 

84.02 

164.78 


0.32 
1.63 


July 24, 1912 
July 6, 1911 


2 . 136 
1.092 
1.035 
1.012 
1.006 


Nov. 24, 1911 
May 31, 1912 
Nov. 22, 1912 
July 24, 1912 
Jan. 13, 1912 



westward elongation is longer than the time from V 1 to V 2 . The 
same thing is true when the earth moves forward in its orbit. And 
similar statements are true for the planet Mercury whose orbit is 
also inferior to that of the earth. Since the orbit of Mercury is 
smaller, these differences just mentioned in the time of passage from 
one elongation to the other are less than in the case of Venus. 

The planets which are nearer the sun than the earth are called 
inferior planets, and those which are farther from the sun, superior 
planets. Suppose an inferior planet is observed at its greatest eastern 
elongation. The question is when will it again be in that favorable 
position for observation. This is its synodical period. It can be 
determined by observations, or it can be computed without difficulty 
from the sidereal period. In the case of a superior planet the time 
for the most favorable observation is in opposition, and after the 
synodical period the planet will have returned to that relative posi- 
tion. Hence, it follows that in order to find the time when a planet 
will be favorably situated for observations it is necessary to know 
once when it was in eastern elongation if it be an inferior planet, or 
in opposition if it be a superior planet, and then to add enough 
synodical periods to arrive at least to the date of computation. For 
example, suppose it were known that Mars was in opposition in 1900 
on a certain date and that its synodical period was exactly two 
years; and suppose in 1911 one wished to know when it would again 
be in opposition. If he added five of the two-year periods it would 
bring the date forward to 1910, which having already passed by 
would not give the observer the information he desired. But adding 



ASTRONOMY 151 

six periods he would find that in 1912 on a certain date Mars would 
again be in opposition, and he could be prepared to observe it. Of 
course, in actual practice the numbers do not come so simply as in 
the example. 

Table VIII gives the sidereal and synodical periods of the 
planets, dates of great eastern elongations in the case of the inferior 
planets, and of opposition in the case of the superior planets. 
From these dates and the synodical periods the times favorable for 
observations of the planets can be determined for as long a period 
as is desired. 

The Two Groups of Planets. It is evident from the preceding 
data, which give a general idea of the solar system considered as a 
whole, that the planets naturally fall into two groups which are 
distinct in many of their characteristics. The first group comprises 
Mercury, Venus, Earth, and Mars, and is called the terrestrial group 
from the general similarity of these bodies to the earth. Jupiter, 
Saturn, Uranus, and Neptune constitute the other group, called the 
major planets because of their relatively great size. The distinction 
in the two groups is seen from the fact that the major planets are on 
the average 17.6 times as far from the sun as the terrestrial planets. 
On the average the terrestrial planets receive per unit area 310 times 
as much heat and light from the sun as the major planets. On the 
average the diameter, surfaces, and volumes of the major planets are 
10, 100, and 1,000 times greater than those of the terrestrial planets. 
The masses of the major planets average 224 times those of the 
terrestrial planets, while their densities are only a little over one-fifth 
as great. The periods of revolution of the major planets average 
77.6 times those of the terrestrial group and, as we shall see, their 
periods of rotation so far as they are known average less than one- 
half of those of the terrestrial planets. These facts are sufficient to 
establish the grouping of the planets which has been adopted. 

Notwithstanding the diversities among the members of the two 
groups of planets, there are many harmonies among all of them 
considered together. The harmonies are fully as important as the di- 
versities. The foremost of the harmonies to be noted is that the 
planets and more than 700 known planetoids all revolve around the 
sun in the same direction and nearly in the same plane. The greatest 
divergencies from the plane of motion are in the case of the planetoids 



152 ASTRONOMY 

The sun rotates in the same direction and, indeed, so do all the 
planets whose rotations are known. The moon revolves around the 
earth in the same direction and rotates in this direction. In fact, 
the satellites of all the planets except one each of Jupiter and Saturn, 
and the satellites of Uranus and Neptune, revolve in this same direc- 
tion. All the orbits are very nearly circular. Often this does not 
strike one as being a fact of any significance, but when it is remem- 
bered that it is just as natural for the orbit of a body moving subject to 
the law of gravitation to have any eccentricity, it does, indeed, seem to 
be a remarkable fact. It is as remarkable as it would be if one were to 
find the trees in a natural forest all arranged in definite straight lines. 
The Planetoids. If the distances of the planets from the sun 
are examined, it will be found that each one is approximately twice 
that of the preceding one with the exception of Jupiter, whose dis- 
tance is about 3.5 times that of Mars. A more exact method of 
finding the relative distances is to take the numbers 0, 3, 6, 12, 24, 
48, and so on, and to add to each of them 4. The sums thus obtained 
are very nearly proportional to the distances of the planets from the 
sun, with the exception that there is a number falling between the 
distance of Mars and Jupiter. This arrangement of numbers, known 
as "Bode's Law," though it was discovered by Titius, led astronomers 
at the end of the eighteenth century to suspect that another planet 
existed between the orbit of Mars and that of Jupiter. Bode's, law 
is not a law in the same sense that the law of gravitation is, for it 
expresses the facts only roughly, and no actual connection between 
them and it has ever been established. However, it was enough to 
direct inquiry toward the existence of an unknown world. In 1800 
a number of German astronomers founded an association whose 
purpose was to search for the unknown planet. The difficulty in a 
problem of this sort arises from the fact that a small planet does 
not look materially different from a star, and it is necessary to find 
in some way whether the object viewed is a star or not. One way 
of detecting it is to find whether the object moves relatively to the 
stars or not. If so, it is not a star. Consequently, one way to find 
whether there are any worlds undiscovered is to make a map of all 
the objects visible with the instruments in use, and then at a later 
date to see whether they have the same positions or not. While the 
discussion of the astronomers was going on, and while they were 



ASTRONOMY 153 

making preparations to carry out extensive observations in the search, 
the philosopher Hegel proved, or at least claimed to have proved, by 
the "most conclusive reasoning," that there were no unknown planets, 
and remarked on the folly of searching for them. Before the German 
astronomers actually got to work, and indeed shortly before the 
publication of Hegel's dissertation, an Italian astronomer, Piazzi, 
at Palermo, discovered an unknown world January 1, 1801, on the 
first day of the nineteenth century. He named it Ceres after the 
tutelary goddess of Italy. 

In 1801, communication was slow compared to that which we 
have at the present time. The news of the discovery of Piazzi did 
not reach Germany until the following spring and by that time the 
sun had passed between the earth and the planet and the latter was 
lost to view. Up to that time it was not known how to compute an 
accurate orbit of a planet from a few observations. The problem of 
getting the orbit of Ceres and the rediscovery of it led a brilliant 
young German mathematician by the name of Gauss to develop a 
method for doing it. In accordance with his computations, which 
directed observers where to look in the sky to find this world, it was 
again picked up. It was found upon examination and measurement 
that its orbit was between that of Mars and Jupiter, at about the 
distance Bode's law would lead one to expect an unknown world to 
be found. The new planet was surprisingly small. According to 
recent measurements of Barnard its diameter is 485 miles. 

In March, 1802, Olbers discovered a second planetoid which he 
named Pallas, and in September, 1804, Harding found a third which 
he called Juno. Olbers discovered again another in March, 1807, 
which is known as Vesta. After the second planetoid was discovered 
it was supposed that perhaps they were the fragments of some larger 
planet which for some unknown reason had exploded. If we imagine 
a planet going around the sun and exploding at some point in its 
orbit, after the explosion the fragments will go on their way around 
the sun in distinct elliptical orbits. But since all elliptical orbits are 
closed they will all return to the point where the explosion took place. 
The period of a planet depends upon the length of its orbit, and as 
the different fragments might move in orbits having different lengths 
they would not all return to the point of the explosion at the same 
time. If this theory were correct, the position in the sky to search 



154 



ASTRONOMY 



for the fragments of an exploded planet would be that where they 
cross. After two planets had been discovered the computations 
showed the two points where their orbits intersected, and conse- 
quently if /the explosion theory were correct, the other fragments 
should be discovered some time at one of these two places. Since 
this theory was at first adopted, though it has long been abandoned, 
the search was prosecuted most carefully in the vicinity of the points 
of intersection of the orbits of the planetoids. 

After the discovery of the first four planetoids no other one was 
discovered until 1845. This world was picked up by Hencke after 




Fig. 75. A Planetoid Trail Photographed at the Yerkes Observatory 

fifteen long years of search. Few men would have the patience to sit 
at the eye end of a telescope night after night and week after week 
for fifteen years before making a discovery. After 1847, catalogues 
of the stars were so extensive that it became a relatively easy 
matter to discover these objects, which were found to be very numer- 
ous. But a new epoch in their discovery began in 1891 when Wolf, 
at Heidelberg, discovered one by photography. The method is 
extremely simple. The photographic plate is given a long exposure 
in a certain region with the telescope following the stars so that 



ASTRONOMY 155 

their images come out on the plate as points. The planetoids move 
among the stars, and if there is one in the field of view its image will 
come out on the plate as a little streak. Fig. 75 shows one of these 
photographs with a planetoid trail at the center of the picture. These 
little trails show planetoids and lead very quickly and conveniently to 
their discovery. In some cases more than one has been found on a 
single plate. There are at the present time over 700 of them known. 

The old theory that the planetoids had their origin in an exploded 
planet has been abandoned because the orbits extend all the way 
from that of Mars out to that of Jupiter, over a distance exceeding 
300,000,000 miles. The planetoids nearest the sun are, at their 
nearest approach to those which are near Jupiter's orbit, more than 
three times as far from them as the earth is from the sun. In fact, 
one was discovered in 1898 whose orbit is between the orbit of the 
earth and that of Mars, and more recently others have been discovered 
whose distances from the sun are equal to that of Jupiter. 

The first planetoids discovered were naturally the largest and 
brightest ones and their diameters were from 100 to 500 miles, 
probably the latter figure being the extreme limit. Those of recent 
discovery are much smaller, probably ranging down to approximately 
10 miles in diameter. The probabilities are that there are unlimited 
numbers of them still smaller. It is impossible to determine their 
mass since they exert no appreciable gravitational influence on other 
known bodies, but if their densities are comparable to those of the 
planets, their combined mass is probably not T f^ that of the earth. 
If it were greater than this its attraction on Mars would sensibly 
disturb the orbit of this planet. Computations referring to these 
planetoids so far discovered, and based on what seem reasonable 
assumptions regarding their density, show that their mass is less 
than 3- oV o" that of the earth. 

Being compelled 1 by the observations to abandon the explosion 
theory of their origin, one might inquire how they have arisen. This 
problem is wrapped up with that of the origin of the planets. Appar- 
ently, the zone between the orbit of Mars and that of Jupiter was 
one in which there was considerable material, but in which no body 
of dominating gravitative influence existed to sweep up and gather 
to itself the widely scattered fragments. We shall take up again the 
question of the origin of the planets. 



156 ASTRONOMY 

The planetoid whose orbit is between that of the earth and 
Mars, known as Eros, presented some remarkable peculiarities to 
astronomers. In February and March, 1901, about three years after 
its discovery, its light began to be variable. At its minimum it was 
less than one-third as bright as at its maximum, and the period from 
maximum to minimum was only 2 hours and 38 minutes; or, 
perhaps, 5 hours and 16 minutes, composed of two sub-periods of 
2 hours and 25 minutes and 2 hours and 51 minutes, respectively. 
In a few months it again was shining with steady light. Since all 
these bodies shine entirely by reflected light, it is difficult to account 
for these variations. One suggestion for explaining them was that 
Eros is really composed of two bodies near together which revolve 
around their common center of gravity. If this were so, when the 
bodies were in a line with us they would present less surface than 
when they were side wise, and consequently would appear fainter. 
But according to this theory it is impossible to account for so great 
variations in the light as the observations actually show existed. 

Another hypothesis for the explanation of the variability of 
Eros is that the reflecting power on various parts of it differs greatly. 
According to this theory, when the highly reflective side is toward us 
it appears bright, and when the duller side, darker. If this were true, 
we should have the period of rotation from the observation of the 
changes in its light. The chief difficulty arises when we attempt to 
explain the large variability for a time, and then later the total 
absence of variability. The orbit of the planetoid is highly inclined 
to that of the earth so that we view it under varying aspects, but in 
spite of this there are real difficulties in explaining the phenomenon. 

One of the uses to which planetoids have been put is to obtain 
a very accurate measurement of the distance from the earth to the 
sun. The relative distances of the planets can all be found without 
knowing any actual distance. In Fig. 66 it was shown how the dis- 
tance from the sun to Venus could be obtained in terms of the 
distance from the sun to the earth. In a similar way all the relative 
distances in the system can be determined. Then, if any actual 
distance either of a body to the sun or from one body to another 
can be found, all the distances become known. It is not easy to 
measure the distance from the earth to the sun directly because the 
sun is a body very poorly adapted for observation. In the first place, 






ASTRONOMY 157 

it is not a point of light and, indeed, has no aosolutely sharp bound- 
ary. In the second place, the light and heat from it shining into 
the instrument disturb the delicate adjustments necessary for mak- 
ing accurate observations. In the third place, it is very far away 
and the difficulties of obtaining accuracy increase with the distance. 
But the first two objections to using the sun as a means of finding 
the distances of the members of the solar system from one another 
are absent in the case of the planetoids; and the third is also absent 
in the case of Eros. Probably the most exact method at the present 
time of finding the distances in the solar system is by measuring the 
distance of Eros. When this planetoid was near to us many observa- 
tions of its position, both visual and photographic, were taken. 
Their reduction at many places, particularly at Cambridge, Eng- 
land, by Hincks, led to remarkably accurate results regarding the 
distance to the sun. It must not be supposed that our knowledge 
of this distance depends upon this method alone, for there are at 
least half a dozen others distinct from it. They all agree in about 
the same distance, though some of them give results which have a 
considerable degree of uncertainty. 

Zodiacal Light and Qegenschein. The zodiacal light is a hazy 
wedge of light stretching up from the horizon along the ecliptic just 
as the twilight is ending or the dawn beginning. The base of it is 
from 20 degrees to 30 degrees wide, and it can be followed under 
favorable atmospheric conditions, when the moon is not in the sky, 
to a distance of 90 degrees- from the sun. Sometimes a narrow, very 
faint band of light three or four degrees wide can be traced entirely 
across the sky. It is very difficult to determine exactly where the 
borders of the zodiacal light are, for it fades out very gradually into 
the darkness of the night sky, and at its brightest is not much brighter 
than the Milky Way. 

The zodiacal light can best be seen when the ecliptic makes a 
large angle with the horizon, and this varies considerably at different 
times of the year. Suppose the sun is at the vernal equinox. It is 
then at the part of its orbit where the ecliptic crosses the equator 
from- south to north. Suppose the sun is setting in the western sky. 
The equator comes up obliquely from the western point on the 
horizon and crosses the meridian at an altitude equal to 90 degrees 
minus the latitude of the observer. The ecliptic comes up from the 



158 ASTRONOMY 

western sky above the equator and crosses the meridian at an altitude 
23.5 degrees greater than that at which the equator crosses. Conse- 
quently it comes up from the western sky more nearly perpendicular 
than the equator does. Since the sun is at the vernal equinox in the 
spring, this is the time of year when the zodiacal light can best be seen 
in the evening. When the sun is at the autumnal equinox the ecliptic 
crosses the equator from south to north and comes up from the 
western sky at sunset very obliquely, being south of the equator. 
At this time the zodiacal light is lost in the haze of the horizon and is 
not conspicuous. If it is desired to observe it in the morning, then 
it is found by similar discussion that the most favorable time of the 

year for seeing it is in the autumn, 
and the least favorable in the 
spring. 

The zodiacal light is probably 
due to a vast number of small 
particles revolving around the sun 
near the plane of the earth's orbit 
and extending out somewhat be- 
yond the path of the earth. In 
Fig. 76 let S represent the sun, E 
-V; ..-.;;.-' the earth, and Z the particles of 

Fig. 76. The Zodiacal Light Is Due to w V,i P V| +Vi P vnrWaon] Vmnrl nf mat- 
Small Particles Revolving around the Sun wmcn tne zoaiacai Dana oi mai- 
near the Plane of the Earth's Orbit ^ j g compose(L Consider an OD- 

server at for whom the sun has recently set. His horizon is //, 
and above H he will see part of the zodiacal band which is illuminated 
by the sun, and it will appear to him as a hazy wedge of light in the 
plane of the earth's orbit, that is, along the ecliptic. 

Die Gegenschein, the German for counter-glow, is a very faint 
oblong patch of light on the ecliptic precisely opposite to the sun. 
It appears like an enlargement of the zodiacal band. It is so very 
faint that it can be seen only under the most favorable atmospheric 
conditions and in the absence of all artificial light. In fact, a planet 
or a bright star near it is enough to make it invisible, and the illumina- 
tion of the Milky Way is absolutely fatal to seeing it. This faint 
object was not discovered until recent times when it was found 
independently by three observers, Brorsen, in 1854, and later by 
both Backhouse and Barnard. One theory for its explanation is 




ASTRONOMY 159 

that it is due to a large number of meteors circulating around a point 
opposite to the sun and about 900,000 miles from the earth. It 
can be shown mathematically that there is a point in this neighbor- 
hood at which a meteor placed and started suitably would always 
stay. If one were started near this point there would be a tendency 
for it to circulate around the point for a time and then to pass on. 
A stream of meteors passing around the sun and near this point would 
be caught in a sort of whirlpool and would circulate around it for a 
time, and give us just such a faint illumination of the sky as the 
gegenschein actually is. While this explanation seems very probable 
we are not absolutely sure that it is correct. 

Probably the observation of the gegenschein is the best test 
of the power of distinguishing faint objects. It can not be seen 
through instruments, because with the telescope only a small part of 
the sky can be observed and no contrast can be obtained. This 
object is from 5 degrees to 10 degrees wide and 10 degrees to 20 
degrees long. The best time for observing it is in the autumn 
months, September and October, when there is no moon in the sky. 

Mercury -and Venus. Having discussed the solar system as a 
whole and the planets in their relations to one another and to the 
sun, it is in order to consider them briefly as individuals. 

Mercury and Venus, being inferior planets, are not situated very 
conveniently for observations because when they are nearest to us 
their dark sides are toward us. On this account the surface mark- 
ings of these bodies are not so well known as those of the superior 
planets, some of which are not near the earth. Mercury can be 
observed best in the daytime. Many faint, dark lines have been 
noted upon it, particularly by Lowell. From a study of these he 
infers that the planet rotates on its axis once during its revolution 
around the sun. The fact that these streaks are visible shows that 
the planet has little or no atmosphere. When it passes between us 
and the sun it appears like a sharp disk on the surface of the sun, 
and this also proves the absence of any atmosphere. This result 
would be expected because the small gravitative power of this planet 
can not hold an atmosphere. 

Another reason for believing that Mercury has no atmosphere 
is that its reflective power is very low. The observations show that 
it reflects only about 17 per cent of the light which falls upon it, which 



160 ASTRONOMY 

is about the same proportion as that reflected, by the moon. 
Apparently a rough surface of broken rock reflects very much less 
light than an atmosphere, particularly if it is filled with clouds. 
Nearly everyone has noticed how extremely bright clouds of the 
thunder-head type sometimes are in the sky. These clouds appear 
very luminous because we see the light side of them. In most cases 
we are on the dark side of clouds, which gives us the impression 
that they are dull and non-luminous. The fact that it is dark below 
them proves that they either reflect or absorb a large part of the 
light, and that consequently if we were on the upper side of them 
they would appear very bright to us. As a matter of fact, the clouds 
are very highly reflective. Anyone who has seen clouds roll around 
a mountain peak knows how much brighter they are than the moun- 
tain unless it is covered with snow. 

The climatic conditions of Mercury are most extreme, espe- 
cially if one side is always toward the sun, as now seems to be the 
case. This side is exposed perpetually to the sun's burning rays 
at a distance where they are about nine times as intense as they 
are on the earth. The other side is never favored by its warmth and 
light. The one side is a region of perpetual torridity and the other 
of continual frigidity. There is a zone around the planet at which 
the sun is near the horizon, where the temperature is more moderate. 
In fact, all intermediate states between the hottest and the coldest 
exist. Almost certainly a planet in the state in which Mercury seems 
.to be can not support life similar to that which flourishes on the 
earth. 

Venus, as distinguished from Mercury, has an extensive atmos- 
phere, as is indicated by its great brilliance, reflecting as it does 
76 per cent of the light which falls upon it, and by the illuminated 
ring which surrounds it when it passes across the sun's disk. Fur- 
thermore, it follows from the kinetic theory of gases that, since 
Venus has a gravitative power at the surface nearly equal to that 
of the earth, it should hold an atmosphere as the earth does. 

It has not been possible to detect many surface markings upon 
Venus because of the extensive atmospheric envelope which smv 
rounds it. At the present time it is impossible to say even what 
its period of rotation is. Some observers have supposed they found 
evidence that it was approximately 24 hours and other observers 



ASTRONOMY 161 

have been equally convinced that their observations have shown 
them that it always keeps the same face toward the sun. If the 
former conclusion is correct the succession of day and night and the 
seasonal changes on Venus are very similar to those of the earth, 
though because of its nearness to the sun the climate should be 
warmer. If the latter conclusion is correct one side should be very 
warm — though not so hot as the corresponding side of Mercury — 
and the other side very cold. The reasons for the difference between 
Venus and Mercury in this respect are, first, that Venus is farther 
from the sun than Mercury is, and second, that the temperature of 
Venus would be largely equalized by the atmosphere. The warm 
air from the heated side would continually pass to the colder side, 
and the cooler air of the dark side back to the heated side. There 
would be a system of trade winds taking the heat 'from the hot to 
the cool side, and the cool air back to the heated side. 

Mars. The planet Mars is at times situated more favorably for 
observations from the earth than any other celestial body except the 
moon. Its distance from the earth at its nearest approach is about 
34,000,000 miles. At this time it is opposite the sun in the sky and 
appears on the meridian at midnight with the illuminated side toward 
the earth. 

The reflecting power of Mars is low, implying in accordance 
with the discussion made above that it has a small atmosphere. 
Other observations confirm this conclusion. Its surface is nearly 
always well visible, showing rarely any indication of clouds. Prob- 
ably the only clouds that are observed are dust storms. 

The explanation for the scanty atmosphere of this planet is that 
its mass is so small and its surface gravity so feeble that it has not 
power to control one. If Mars does control an atmosphere, probably 
it is made up largely of the heavier gases. When Mars passes between 
us and a star the light of the star is suddenly extinguished as the 
edge of Mars reaches it. If Mars had an extensive atmosphere the 
light of the star would gradually diminish as it shone through more 
and more of the gaseous envelope surrounding the planet. Probably 
atmospheric pressure on Mars does not exceed that on the top of 
our highest mountains. 

The planet Mars is at times so near us and it is so free from 
an obscuring atmospheric envelope that it has been possible for a 



162 ASTRONOMY 

long time to secure accurate observations of its surface markings. 
Fig. 77 shows a series of photographs (made by Barnard with the 
great 40-inch Yerkes telescope) of one side of Mars on which can be 
seen large shaded areas with a peninsular projection similar to that 
of the Indian Peninsula in southern Asia. The light-colored part of 




Fig. 77. Mars as Photographed with the Great Yerkes Telescope by Barnard 

Mars is actually a sort of dull brick-colored red, and it is this which 
gives it its ruddy appearance in the sky. The shaded areas have a 
slightly greenish tinge. From observations of the motions of these 
markings across the disk of the planet it has been possible to find 
its period of rotation with a very high degree of accuracy, and also 
the inclination of its equator to the plane of its orbit. The day of 



ASTRONOMY 163 

Mars is 24 hours, 37 minutes, 22.7 seconds long, reckoned in our 
mean solar time. The inclination of the plane of the equator of Mars 
to that of its orbit is about the same as the inclination of the ecliptic. 
Therefore, except for the greater distance of this planet from the sun, 
its days and seasons succeed one another about as the days and 
seasons of the earth run through their cycles. 

Besides the dark-shaded areas observed on the planet, there are 
other remarkable details which have been seen in recent years. In 
1877 Schiaparelli, an Italian observer, working with a modest tele- 
scope of 8.75 inches aperture, but favored with the transparent 
Italian skies, found that Mars was crossed and recrossed by many 
dark-greenish streaks which always began and ended in the dark 
areas mentioned above. These streaks were of great length and 
invariably extended in straight lines, that is, along the arcs of great 
circles. They varied from a few hundred miles in length up to 
nearly 4,000. These streaks were called by Schiaparelli canali 
(channels), which was unfortunately translated into "canals," a 
designation altogether too suggestive, for there is no guarantee that 
they have any analogy with canals on the earth. The very narrowest 
of them are 15 or 20 miles across, and when a number intersect at a 
point there is generally, if not always, a dark knot at the points of 
intersection. For example, seven canals converge in Lacus Phoenicia 
and six in Lacus Lunae. According to Lowell the junctions of canals 
are always provided with these spots, called "lakes," and conversely 
lakes are never found except at the junctions of canals. 

In the winter of 1881-82 Mars was again in favorable position 
for observation and Schiaparelli studied it attentively a second time. 
He not only confirmed his preceding observations, but he found that 
in many cases there were two canals running parallel to each other 
for long distances. This doubling was found to depend upon the 
seasons and to develop with astonishing rapidity especially when the 
sun was at the Martian equinox. 

The observations of Schiaparelli have been, in a general way, 
confirmed by Lowell and have been greatly extended by him during 
fifteen years of observations at Flagstaff and in Mexico with a tele- 
scope of 24 inches aperture. He has found in addition to the canals 
observed by Schiaparelli many others, bringing the total list now up 
to over 400. Lowell describes these streaks as verv narrow and 



164 



ASTRONOMY 



thread-like, and of remarkable uniformity. Fig. 78 shows the net- 
work of canals which Lowell discovered on Mars from many obser- 
vations and recorded in a single drawing. 

On the whole, other observers, many of whom have had wide 
experience and have been provided with large instruments, have not 
been able to confirm the observations of Schiaparelli and Lowell. 




Fig. 78. Mars from a Drawing by Lowell 

This negative evidence must be given considerable weight, though, of 
course, positive evidence should always be regarded as the more val- 
uable. There have been many astronomers who have expressed the 
opinion that in some way the observers who have seen the line-like 
markings on Mars have been deceived, and that no such features ex- 
ist there. Experiments have shown that if a number of small mark- 
ings be placed irregularly on a disk, and the disk placed at such a dis- 



ASTRONOMY 



165 



tance that they are just beyond the limit of distinct visibility, then an 
observer seeing it will by some process integrate the fine markings 
into lines. Though lines do not exist on the object at which he looks, 
he will apparently see them under these circumstances. Because of 
this fact, the suggestion has been made that Mars is covered with a 
large number of fine spots which are slightly beyond the limits of dis- 




Fig. 79. 



The Disappearing Polar Caps of Mars as Observed by Barnard at the Lick 
Observatory in 1894 



tinct vision and that the eyes, particularly of some observers, integrate 
them and give them the appearance of many lines. Of course, this 
conclusion is not a necessary consequence of the experiments. 

Besides the canals on Mars, the most interesting other feature is 
the changing polar caps. When the autumn of a hemisphere of the 
planet comes on, the polar region extending down 25 degrees to 35 



166 ASTRONOMY 

degrees from the pole is covered with a white mantle, shining with 
the brilliance of snow. This white covering appears suddenly, remains 
all winter, and disappears gradually in the spring, sometimes entirely 
vanishing at midsummer. It is entirely absent during the summer 
and reappears again rather suddenly in the autumn. Fig. 79 shows 
a series of drawings of the diminishing polar cap made by Professor 
Barnard in 189-1 at the Lick Observatory. The slight irregularities 
in its outline prove at least a certain degree of roughness of the 
surface of Mars. While these polar caps have every appearance of 
being made of snow, there is some doubt whether this is the true 
explanation or not. In the first place, there is very little if any 
water upon the planet. In the second place, it is not perfectly certain 
that if there were water it would be transferred in clouds from one 
region to another and precipitated in the form of snow, though perhaps 
this is not an unreasonable conclusion. But the most serious question 
in the interpretation of these polar caps, is that apparently the climate 
of Mars ought to be considerably colder than that of the earth. 
Mars is so much farther from the sun than the earth is, that it 
receives less than half as much light and heat from the sun as the 
earth. Using this fact to compute the theoretical temperature which 
it would have if its atmospheric conditions were the same as those 
of the earth, and assuming that the mean temperature of the 
whole earth is 60° F., it turns out that the average temperature on 
Mars should be 38 degrees below zero. With such a temperature as 
this as an average for the whole planet, taking summer and winter 
together, it is clear we should not expect the polar cap entirely to 
disappear, inasmuch as on the earth it is a permanent feature. Of 
course, the different constitution of the atmosphere of Mars might 
account for a considerable difference, but it certainly would seem to 
strain the probabilities to suppose that a very rare atmosphere would 
have such a constitution that it could make a variation in the mean 
temperature of a planet of 60+38 = 98° F. And even this is not 
enough to account for the entire disappearance of the polar cap. 

One suggestion made for explaining the polar cap of Mars is 
that it is carbon dioxide which freezes at a temperature of 109° F. 
If the atmosphere of Mars contains this compound, and if the tem- 
perature falls below this point, it would freeze and be deposited on 
the surface as a white substance resembling snow. But as was 



ASTRONOMY 167 

mentioned in connection with the discussion of the earth's atmosphere, 
carbon dioxide is one of the atmospheric substances which tends to 
produce a high mean temperature. It is thus apparent that this 
theory is at least to some extent contradictory to itself. At the present 
time we are not justified in drawing any positive conclusion about the 
meaning of the polar cap or the climatic conditions on Mars. 

Assuming that the polar cap is snow and that the canals on Mars 
actually exist as they are seen by a few observers, the question of 
their explanation becomes ore of considerable interest. W. H. Pick- 
ering suggested the idea that the canals are streaks of vegetation. 
This conclusion is to some extent supported by the fact that they 
appear in the spring, remain visible during the summer, and disappear 
in the autumn. Lowell pushes the theory much further by supposing 
that the canals are streaks of vegetation which grow because the 
territory where they appear is irrigated. This implies the existence 
of life and a high order of intelligence on Mars. He supposes that 
these intelligent creatures have dug waterways from the dark regions, 
which he interprets as being marshy regions, for hundreds and in 
some caees thousands of miles, out across the brick-red parts, which 
he interprets as being burning deserts. Leading out from the sides of 
these irrigation ditches he supposes there are lateral canals which 
reach to a distance of 10 to 25 miles. In this manner he supposes 
a streak from 15 to 50 miles wide and from a few hundred to three 
or four thousand miles long is irrigated. In the winter time vegetation 
would be dead, certainly if it were analogous to that on the earth, 
and the streaks would be invisible. As the spring approaches, the 
polar caps would melt and the marshy regions would fill up, the 
water would be led out through the main irrigation ditches and into 
the laterals, thus supplying the ground with the moisture necessary 
for the development of vegetation. Having then the increasing 
warmth and the needed supply of water, he supposes vegetation 
would spring up and flourish. This would give the areas on which it 
grew a dark color, as contrasted with the red of the soil. The places 
where the canals cross would be irrigated regions of unusual size and 
probably would be the seats of considerable population. 

Lowell's theory is interesting, even if it is somewhat fantastic. 
There are serious difficulties in the way of accepting it, aside from 
the question of the climatic conditions on the planet. One of these 



108 ASTRONOMY 

is that it is not a sign of intelligence to construct canals thousands of 
miles long, in straight lines, and of uniform width, irrespective of the 
irregularities of the surface of the planet and the variations in the 
fertility of its soil. The irregularities of the borders of the polar cap 
prove that the surface is far from being smooth, and in fact the 
division of it into red regions and dark regions shows that it is by 
no means uniform. It is reasonable to suppose, in view of what we 
know of the earth and the moon, that all of it is more or less 
irregular. If it has had an origin similar to that of the earth, and if 
it has had an evolution similar to that of the earth, then the character 
of its soil should vary from place to place, like that of the earth. 
Certainly these are the probabilities. It seems most remarkable, 
then, that these creatures who are assumed to be intelligent should 
make their canals of absolutely uniform width and in absolutely 
straight lines. Besides, it is not evident why it is economical to run 
canals 3,500 miles from the source of water, when there is abundant 
unirrigated territory in the immediate vicinity. The expense of this 
is certainly enormous. If vegetation requires the same amount of 
water there that it does on the earth in order to nourish, the canal 
system and Lowell's interpretation of it imply that, for every ton of 
vegetable matter that is raised on Mars, on the average one thousand 
tons of water are transported along the canals one thousand miles. 
It is only fair to the reader to state that while Lowell has urged his 
views very strongly, astronomers are almost universally extremely 
skeptical regarding them. 

Granting that Lowell's theory is correct, one is still likely to 
draw quite erroneous conclusions. If there is life on Mars and a 
high order of intelligence, there is no reason to suppose that the 
beings of highest intellectual development are physically anything 
like men. The animals on the earth, and human beings among them, 
are adapted to their surroundings, for if they were not more or less 
perfectly adjusted to them they would perish. For example, our 
skeletons are made of bones strong enough to support us and permit 
of certain activities when we are subject to certain gravitative forces; 
our lungs are adjusted to the atmosphere in which we live; and the 
amount of water on the earth and in its atmosphere is an important 
factor in the life processes, and animals on the earth are adjusted 
to these conditions. On the planet Mars nearly all of the fundamental 



ASTRONOMY 



169 



conditions are radically different from those on the earth. For 
example, the surface gravity is much less, the atmospheric pressure 
is only a small fraction of what it is here, the constitution of the 
atmosphere may be quite different, the intensity of solar radiation 
is less than half that on the earth, and the amount of water is a very 
small fraction of that on the earth. Consequently, if life does flour- 
ish on Mars, then it must physically be very different from that on 
the earth. Of course, there is no fundamental reason why it should 
not be different. 

Granting that there is life on Mars and that in its physical 
aspects it is suited to its environment, we are still likely to draw 
erroneous conclusions regarding the organization of what we may 
call its society. There is no reason for assuming that there are social 
and political conditions on another planet anything like those which 
are on the earth. If there is life there, thousands or millions of years 
ago it may have passed through that stage of evolution correspond- 
ing to the one in which we now struggle. When one thinks of the 
remarkable changes which society has undergone in a few centuries, 
the significance of such a statement becomes clear. At the rate 
human relations have been changing, in a few thousand years from 
now social conditions will be ab- 
solutely unlike those existing at 
present. Hence, it is clear that 
even though the physical condi- 
tions on another world were like 
those here, there would be no 
reason for assuming a general 
similarity in the mode of life and 
state of society. 

The planets Mercury and 
Venus have no satellites, so far 
as known, but Mars is attended 
by two very small moons re- 
volving from west to east 

around it sensibly in the plane of its equator. They are so 
small and so near the bright planet that they were not dis- 
covered until 1877, when Hall found them with the great telescope 
of the Naval Observatory at Washington. They can be seen 




Fig. 80. The Orbits of the Satellites of 
Mars and the Planet on the Same Scale 



170 ASTRONOMY 

only with a few of the largest telescopes in the world. Hall named 
these satellites Phobus and Deimos. Phobus is 5,850 miles from 
the center of the planet, or only 3,750 miles from its surface. Deimos 
is distant 14,050 miles from the center of the planet. Fig. 80 gives 
the planet and the orbits of its two satellites to scale. 

The diameters of the satellites of Mars are probably approxi- 
mately ten miles. They are so small that they can not be measured 
directly, and can only be inferred from the amount of light they 
send us. On a body so small as these satellites and having the 
density of the earth, an object which would weigh one pound on the 
earth would weigh only -gV of an ounce. 

One consequence of the nearness of the satellites to the planet 
is their rapid revolution around it. The period of revolution of 
Phobus is 7 hours and 39 minutes, and that of Deimos 30 hours 
and 18 minutes. It follows from this that Phobus goes around the 
planet in about one-third of its period of rotation. Phobus and the 
planet both go to the east, but Phobus the faster. Therefore, the re- 
markable situation is realized of a satellite rising in the west and 
setting in the east. The period of Phobus from meridian around to 
meridian again is 11 hours and 7 minutes, or a little less than 
half a day. This satellite then runs through all the changes of its 
phases between sundown and sunrise. On the other hand, Deimos, 
whose period is longer than that of the rotation of Mars, rises in the 
east and sets in the west, the mean period from meridian to meridian 
being 131 hours 15 minutes. 

Jupiter. Jupiter is a very bright object in the sky, its mag- 
nitude depending upon its great size and the high reflective power 
of its surface. When the computations are made it is found that 
Jupiter reflects about two-thirds of the sunlight which falls upon it. 
From this it can be inferred that it has an extensive atmosphere. 
This conclusion is supported by many other considerations. The 
mean density of the planet is very low and probably we never have 
seen its solid surface if, indeed, it has any. 

As seen through a telescope Jupiter is characterized by a series 
of bright bands, alternately light and dull brown, running parallel 
to its equator. These bands vary in width and number, but are 
generally from 1,000 to 10,000 miles wide. They are most con- 
spicuous near the equator, and the equator is generally covered by a 



ASTRONOMY 



171 



light band. At the present time it is 8,000 or 10,000 miles wide. 
In 1882, according to the drawing of Hough, who for many years fol- 
lowed this planet carefully, the equator was entirely covered by a 
union of the dark bands which are on each side of it. Fig. 81 shows 
Jupiter as it has appeared in recent years. 

One of the most conspicuous features ever seen upon Jupiter 
is what is known as the great red spot, which was until recently a 
pale pinkish oval extending parallel to the equator for 30,000 miles 
and in the opposite direction 7,000 miles. It appeared rather sud- 
denly in 1878 beneath the southern red belt. In a year after its 
appearance it had changed to a bright red color, and was the most 




Fig. 81. The Planet Jupiter as Drawn by Barnard 

conspicuous object visible on the planet. Since that time it has 
undergone many changes both of color and brightness, and though 
much diminished in intensity, is yet generally faintly visible. 

From observations of the spots and other distinct markings 
on Jupiter the period of its rotation on its axis has been found to 
be on the average about 9 hours and 54 minutes. No other celestial 
body is known whose period of rotation is so short as this. It is 
necessary to speak of the rotation on the average because there are 
great variations among the spots, particularly when they are in 



172 ASTRONOMY 

different latitudes. Some markings have been observed which give 
a period of 9 hours 50 minutes, while others give a period so long 
as 9 hours and 57 minutes, or an extreme difference of about gr of 
the whole period. And since the circumference of the whole planet 
is nearly 300,000 miles, it follows that the rate of rotation at the 
equator is about 30,000 miles an hour. Therefore, two spots whose 
difference in motion is -gV the motion of either have a drift relative 
to each other of about 350 miles per hour. On the earth the most 
violent tornadoes we ever have are produced by wind velocities 
not much exceeding 100 miles an hour. The variation in the rate of 
rotation of the different parts of Jupiter is not entirely irregular. 
As a rule the equatorial parts rotate most rapidly. There are, 
however, some dissimilarities between the two hemispheres. On 
the whole the southern hemisphere presents evidence of more rapid 
changes in the spots, and perhaps greater relative motions among 
them. More remarkable than these variations in motion from spot 
to spot, is the fact that sometimes the rate of motion of a single spot 
changes considerably. For example, the period of rotation of the 
great red spot increased seven seconds in the first eight years follow- 
ing its discovery, but since that time it has remained sensibly con- 
stant. There is no conclusive explanation of the reason why the 
various zones of Jupiter rotate with different periods, or why the 
rates of rotation of the different spots vary from time to time. 

It follows from the low density of Jupiter and the relatively 
rapid changes on its surface that there are probably no fixed features 
on it whatever. Probably this planet is largely gaseous, though the 
pressure at great depths is so great that it may be the laws of gases 
are not strictly obeyed. The surface gravity is 2.6 times that of the 
earth, and this indicates that there are enormous pressures in the 
depths of the planets. The fact that Jupiter has a low density in 
spite of high pressures, leads to the conclusion that either this planet 
is made up largely of very rare materials, or that it has a very high 
temperature. It has often been supposed that its surface is itself 
hot and partly self-luminous. One can scarcely escape this conclu- 
sion when he looks into the sky at Jupiter and sees how exceedingly 
brilliant it is. It stretches his imagination to believe that the light 
which he sees is all sunlight which has been reflected from the sur- 
face of the planet. Nevertheless, it is certain that Jupiter radiates 



ASTRONOMY 173 

directly no sensible quantity of light. As we shall see, this planet has 
many satellites and when they pass between it and the sun their 
shadows fall upon it. If Jupiter were self-luminous the places where 
the shadows strike would still be bright, the brightness depending 
upon its luminosity. But the actual observations show that where 
the shadows fall Jupiter is very black indeed. If the satellites should 
pass into the shadow of Jupiter, they would be st 11 somewhat il- 
luminated if Jupiter itself were luminous, but we find that if they 
pass behind Jupiter so that all the sunlight is cut off from them, they 
instantly become totally invisible. From this we conclude that, 
although the planet may be very hot throughout most of its volume, 
its surface is yet so cool that it gives out no sensible quantity of light. 

The inclination of the plane of Jupiter's equator to that of its 
orbit is only three degrees. The eccentricity of its orbit is very small. 
Consequently there are no marked seasonal changes on this planet. 
Jupiter is a little more than five times as far from the sun as the earth 
is, and therefore gets less than yj as much light and heat. If it were 
situated similarly to the earth and had an atmosphere similar to that 
which surrounds the earth, its mean temperature would be extremely 
low. If planets go through an evolution from those primitive condi- 
tions in which we find Jupiter at the present time to those the earth is 
in now, and perhaps on to dead worlds like the moon, certainly Jupiter 
when it loses its heat will lapse into a condition of perpetual frigidity. 

Jupiter is surrounded by a remarkable family of satellites. 
Four of them are large, ranging in diameter from 2,000 to 3,600 
miles. They were the first celestial objects ever discovered with 
a telescope, and were first seen by Galileo in 1610. They are barely 
beyond the limits of visibility without optical aid and, indeed, could 
be seen with the unaided eye if they were not lost in the dazzling rays 
of the planet. No other satellite of Jupiter, besides these four, was 
discovered until 1892 when Barnard, then at the Lick Observatory, 
caught a glimpse of a fifth one very close to the planet. It is so small 
and so buried in the rays of the great planet that it can be seen only 
by experienced observers through a few of the largest telescopes in 
the world. Since 1905 three new satellites revolving at great dis- 
tances from the planet have been discovered. Two are at a distance 
of about 6,500,000 miles from the center of the planet, and the third 
is distant about 12,000,000 miles. 



174 



ASTRONOMY 



The distances of the satellites range from 100,000 miles to 
12,000,000 miles; the periods from about 12 hours to 550 days. The 
periods are much shorter than they would be for a planet of a smaller 
mass. For example, the satellite nearest Jupiter of the four which 
Galileo discovered, which is numbered 1 and named Io, revolves at 
a distance of 261,000 miles. This is a little greater than the distance 

of the moon from the earth, 
but in spite of this fact its 
period instead of being 27 
days is less than 2s days. 
This is, of course, due to the 
greater attractive power of 
the planet Jupiter, and, as 
was explained above, gives 
us a means of determining the 
mass of Jupiter. Fig. 82 gives 
Jupiter and the orbits of the 
five inner satellites to scale. 

A very remarkable dis- 
covery was made in connec- 
tion with Jupiter's satellites, 
in 1675, by the Danish astronomer Romer. The period of revo- 
lution of Jupiter's satellites can be determined from the times 
when they pass into the shadow of the planet and become invisible. 




Fig. 82. 



Jupiter and the Orbits of Five of Its 
Satellites on the Same Scale 




Fig. 83. The Discovery of the Velocity of Light from Eclipses of Jupiter's Satellites 



Their periods were determined when the earth was on the side of 
its orbit towards the planet, as at E 1 in Fig. 83. Having deter- 
mined the period, it was possible to predict the times when the 



ASTRONOMY 175 

eclipses should occur. A few months later when the earth got to the 
position E 2 , and Jupiter to J 2 , it was found that the eclipses did not 
occur at the predicted times, but a few minutes later. It was inferred 
from this that the reason they were delayed was not that the satellites 
moved around Jupiter with different periods, but that the light had 
farther to come to the earth. After the satellite passes into the 
shadow of Jupiter, it is still visible to the earth until the last light 
which leaves it before it passes into the shadow, reaches the earth. 
The distance from J 2 "to E 2 is nearly 180,000,000 miles greater than 
the distance from J \ to E v Consequently, if light does not travel 
with infinite speed, the eclipses should be as many minutes late when 
observed from E 2 as it takes light to travel over the difference cf 
these distances. It was found from the calculations that the obser- 
vations could be explained under the theory that light travels at 
the rate of about 200,000 miles per second. 

The finite velocity of light has been proved in many other 
ways. It has not been necessary to appeal to celestial phenomena 
in order to determine its rate, but it has been measured on the sur- 
face of the earth by a number of experimenters. The work of Fizeau, 
Michelson, and Newcomb shows that the velocity of light is very 
nearly 186,330 miles per second. It follows from this that it takes 
light about 499 seconds, or a little more than 8 minutes, to come 
from the sun to us. Therefore, when anything takes place upon the 
sun it is not seen here until 8 minutes later. The distance of 
Jupiter is so great that it takes about an hour and a quarter for light 
to go to it from the sun and back to the earth. 

Saturn. In many respects Saturn is the most interesting 
planet in the solar system. It is distinguished by a remarkable 
system of rings which surround it in the plane of its equator. Fig. 
84 shows the general appearance of the rings according to a drawing 
made by Barnard. The extreme diameter of the outer ring is approxi- 
mately 175,000 miles. Between the outer ring and the brightest one 
is a vacant space about 2,200 miles in width. This is known as 
Cassini's division, having been discovered by the French astronomer 
Cassini. Inside of Cassini's division is the brightest ring, whose 
width is about 18,000 miles. Near its exterior it is*brilliantly luminous, 
shining as brightly as the planet itself, but it fades out gradually 
toward its interior border. Inside of the bright ring is a fainter ring 



176 



ASTRONOMY 



known as the crepe ring, which was discovered simultaneously in this 
country and in England about fifty years ago. Its width is about 
11,000 miles. Then between the inner edge of the crepe ring and the 
planet is a gap of about 6,000 miles. 

The ring is very thin, as is shown by Barnard's drawing, Fig. 
85, when it was almost edgewise to the earth in 1907. When it 
was exactly edgewise it became invisible even through the great 
Yerkes telescope. It follows from this that its thickness can not 
exceed 50 miles. If one should draw a map of Saturn and the ring 
system, making the whole diameter of the ring system five inches, 
on the same scale the thickness would be only fho of an inch. 




Fig. 84. Saturn and Its Rings from a Drawing Made by Barnard 

The bright rings appear to be as solid and as continuous as the 
planet itself. For many years after their discovery by Galileo, it 
was supposed that they were perhaps composed of solid or liquid 
material. It was proved by Laplace that such a constitution is 
impossible. If they were solid the attraction of the planet would crush 
them unless they were made of stronger material than anything we 
know. It is easy to see that a solid ring is dynamically similar to 
an arched bridge, the difference being that the ends of it do not rest 
upon the planet but upon other portions of the ring. If the ring is 
supposed to rotate around the planet the difficulties are relieved to 
some slight extent. If it is supposed to rotate fast enough so that 



ASTRONOMY 177 

the centrifugal acceleration of the interior part balances the attrac- 
tion of the planet for it, then the centrifugal acceleration of the outer 
part will be much too great and there will be a tendency for it to fly 
into fragments. Even if it were made of material a hundred times 
stronger than any material with which we are familiar on the earth, 
still it could not remain permanent in that form if it were in the solid 
state. A liquid state is equally impossible. Consequently there re- 
mains only one hypothesis, and that is that it is made up of a vast 
swarm of small particles circulating around the planet in the plane 
of the planet's equator. This theory was suggested nearly two hun- 
dred years ago but was not generally adopted until recent times. 
Under this hypothesis every separate particle moves like a satellite 




Fig. 85. The Rings of Saturn When They are Nearly Edgewise Toward the 
Earth— After a Drawing by Barnard 

free from all the others except at times of possible collision. Accord- 
ing to this theory those particles which are nearest the planet move 
most rapidly, and those which are farthest move most slowly, and 
the difference is a precise amount depending upon the attraction of 
the planet and the difference in distance. It is possible to compute 
theoretically what this difference should be. About 20 years ago 
the spectroscope was used to determine how these particles moved, 
and it was found that their motions were in perfect harmony with the 
theory that the rings are made up of a great swarm of small particles 
which revolve independently of one another. 

It might be supposed that there are difficulties in accounting 
for the appearance of solidity of the rings of Saturn on the dust- 



178 ASTRONOMY 

cloud theory. One might imagine that they should be more nearly 
transparent than they are. But the incorrectness of this view is at 
once evident when we consider how opaque are the clouds in our 
own atmosphere. Clouds are made up of small drops of water in 
great numbers and form opaque screens, though often they are not. 
more than half a mile thick. Consequently, it is easy to see how 
a swarm of dust particles, possibly as much as fifty miles in thick- 
ness, might have the appearance of being perfectly solid. With 
such a thickness it is not necessary to suppose the particles are very 
close to one another or that collisions very frequently take place. 

The planet itself is somewhat similar to Jupiter, though the 
markings on it are less distinct. There is a bright equatorial belt 
and many slightly darker zones in the higher altitudes. The polar 
regions are generally darker than any other part of the planet. It 
has been difficult to find spots which are lasting enough and con- 
spicuous enough to enable the observers to determine the period of 
Saturn's rotation. But those determinations which have been made 
show that this planet rotates on its axis in a little more than 10 hours. 
It is also similar to Jupiter in the fact that its equatorial zone rotates 
more rapidly than its higher latitudes. Likewise there are relative 
drifts of different parts at high speed. Some portions have been 
observed to pass by others at the rate of 600 or 700 miles per hour. 

Since Saturn has a density considerably less than water one 
would not expect to find in it any solid material, at least near its 
surface. The changing and unstable character of the markings 
which are observed harmonizes perfectly with this conclusion. It 
is almost certain that Saturn is gaseous to a great depth, and per- 
haps throughout. The planet is certainly in an early stage of its 
evolution and will not become suitable for the existence and develop- 
ment of life until after it undergoes enormous changes. 

The plane of Saturn's equator is inclined to that of its orbit by 
27 degrees. For this reason the seasonal changes would be marked. 
But Saturn is so far from the sun that it receives only -9V as much 
light and heat per unit area from the sun as the earth does. It fol- 
lows that if its atmospheric constitution were anything like that of 
the earth it would be continually frozen, even in its equatorial 
regions, and consequently that the seasonal changes would not be 
important. But here, as in the consideration of all the planets, the 



ASTRONOMY 



179 



constitution of the atmosphere is an important factor which must 
not be neglected. 

Saturn has more known satellites than any other planet. The 
last two of the ten were discovered by photography. The one nearest 
to Saturn is distant from its center 117,000 miles; the one farthest 
is distant about 8,000,000 miles. Their periods of revolution vary 
from about 225 hours to 550 days. The periods are shorter than 
they would be for satellites revolving around the earth at the same 




Fig. 86. Saturn's Satellite System, with the Exception of the 
Ninth, on the Same Scale 

distances, but somewhat longer than they would be for planets 
revolving around Jupiter at the same distances. These satellites 
vary in diameter from 100 or 200 miles to 3,000 miles. Fig. 86 is a 
map of Saturn's satellite system (with the exception of the ninth 
which is so far away it can not be shown) in which the dot at the 
center represents the planet. A remarkable thing about these 
satellites is that all of them revolve from west to east with the excep- 
tion of the ninth which revolves in the opposite direction. 

Uranus. Uranus is so far from the sun that it appears in the 
sky as a faint object of the sixth magnitude. It was discovered in 
1781 by Sir William Herschel, who was then carrying out his pro- 



180 ASTRONOMY 

gram of sweeping the whole sky for interesting objects. Herschel 
as a young man was a professional musician and originally took up 
astronomy only as a pastime. His imagination became fired by the 
mysteries of the heavens and he determined to explore them so far 
as was in his power. In those days it was not possible to buy a tele- 
scope for a relatively small amount of money, as it is now. Con- 
sequently, if he were to have an instrument he must make it himself. 
Accordingly, he took up the study of the theory of optical instru- 
ments and of other branches of mathematics and astronomy. With 
his own hands he made many telescopes. It was with one of these 
that he discovered the planet Uranus. One night in his sweeping 
of the sky he detected an object which, though nearly like a star, 
differed from a star in having a very small disk. Through a tele- 
scope, no matter how powerful it may be, the stars still appear as 
points of light, though, of course, much brighter than without an 
instrument. But the planets have sensible disks, their apparent size 
depending upon their actual size and their distance from the observer. 
Now, Uranus is so far away that its disk is apparently very small 
even when seen through a large telescope. It is remarkable that 
Herschel should have noticed that it differed in appearance from a 
star. At first he did not suspect that he had found a new planet. He 
informed his friends of the peculiar object which he had seen and 
expressed his opinion that it might be a comet. If it were not a 
star its position would change rapidly with respect to them. Obser- 
vations showed in a few days that it was moving and in a few 
weeks that instead of being a comet it was, indeed, a new planet. 
This was the first world discovered in historic times. It immediately 
attracted the widest interest. George III., who was then king of 
England, appointed Herschel royal astronomer and he thenceforth 
devoted all his life to the study of astronomy. 

Four satellites have been discovered revolving about Uranus. 
They all move sensibly in the same plane, which is almost at right 
angles to the plane of the planet's orbit. If the planet's equator 
is in the plane of the orbits of the satellites, as we may perhaps infer 
from analogy with the other planets, particularly Jupiter and Saturn, 
then the inclination of its equator to the plane of its orbit is about 
90 degrees. A planet with such a relation of its axis of rotation to its 
plane of revolution would not have seasons in any respect similar 



ASTRONOMY 181 

to our own. However, this is not an important question in the case of 
a planet so far from the sun as Uranus is, because if the surface con- 
ditions and atmosphere are at all similar to those of the earth, its mean 
temperature must be many degrees below zero even at the equator. 

Uranus is so far from the sun and the earth, being at its nearest 
to the earth about 1,600,000,000 miles away, that no surface markings 
have been detected on it by means of which its rotation can be deter- 
mined. The only hope at present of finding its rate of rotation is 
from the effects of an equatorial bulge, which is a consequence of 
a rotation, on the motion of the satellites which revolve around it. 
These effects are so small that it is questionable whether accurate 
results can be obtained by them or not. Little is directly known 
regarding the physical condition of Uranus except its density. Per- 
haps an exception to this statement should be made because, when 
the light which is received from it is analyzed by the spectroscope, 
it is found that the atmosphere of Uranus has subtracted some of the 
light. The part of the light which is absorbed in this way depends 
upon the constitution of the absorbing gas. From a study of its light, 
made particularly at the Lowell Observatory, it is inferred that 
Uranus has an extensive atmosphere made up to a considerable degree 
of light gases. It is found from the observations that Uranus reflects 
about 60 per cent of the sunlight which falls upon it, and this also 
goes to support the conclusion that it has an extensive cloud-filled 
atmosphere. 

Neptune. Neptune is the most remote planet from the sun, so 
far as is known, and is most inconveniently situated for observations 
from the earth. No surface markings on it have been detected and 
nothing is known regarding the character of its surface or the rate 
of its rotation. From its low mean density, high reflective power, 
and the character of the light its atmosphere absorbs, it is inferred 
that it has surrounding it an extensive atmosphere of light gases. 
It has one known satellite which revolves around the planet in a 
period of about six days and which has a diameter of about 2,000 
miles. The plane of the satellite's motion is inclined to the plane 
of the orbit of the planet by 35 degrees, and it moves in the retro- 
grade direction. If the satellite is in the plane of the planet's equator, 
and if the planet rotates in the direction of the satellite, it is the only 
example known of a planet rotating backward. 



182 ASTRONOMY 

The discovery of Neptune, made in 1846, was the result of one 
of the most brilliant predictions ever made in science. Irregularities 
in the motions of Uranus led to it. As was explained in connection 
with the discussion of the planetoids, the orbit of a planet can be 
found from a few observations, and its position thereafter can be 
predicted for any length of time, however great. After Herschel 
discovered Uranus and had made a sufficient number of observations 
of it to enable mathematicians to compute its orbit, its theoretical 
position was calculated for many years. By 1820, or 40 years after 
its discovery, it was found that the planet was deviating a little from 
its predicted path. By 1830 the deviation was a little greater, and 
by that time had become sufficiently large to seriously disturb 
astronomers. This does not mean that mathematicians predicted 
Uranus would be seen in one part of the sky and that it was actually 
seen in quite another, but that the deviation was enough so that it 
could be observed with a telescope. As a matter of fact, the planet 
was actually observed so near its theoretical position that the differ- 
ence was quite beyond the limits of visibility without a telescope. 
That is, if a star were in the predicted place and another in the 
observed place, the two would be seen as one without optical aid. 
The exactness of astronomical science is shown by the fact that so 
small a disagreement between theory and observation as this should 
have caused astronomers so much unrest. 

The explanation of the discrepancy between theory and observa- 
tion was not easy to make. However, shortly after 1830 a German 
astronomer, named Bessel, suggested that perhaps Uranus was 
deflected from its predicted path because of the attraction for it of 
an unknown planet situated out beyond it. The problem of finding 
the position of the unknown planet from so slight an irregularity as 
was observed in the motion of Uranus, was one of immense difficulty, 
and one which no one at the time had the courage to undertake to 
solve. The matter rested for about ten years and then two young 
men undertook the solution of the problem. One was Adams of 
Cambridge, England, and the other, Leverrier, of Paris. They began 
work on the problem, each entirely independent of the other, and 
without knowledge that the other was undertaking it. Adams 
finished his results first, in 1845, and found where the unknown 
world must be. He took his figures to English astronomers who had 



ASTRONOMY 183 

telescopes and asked them to search for it. He did not succeed in 
arousing any particular interest, nor in having active steps taken in 
the search. Being somewhat discouraged by the rebuffs he met, he 
let the matter rest. In the meantime Leverrier finished his compu- 
tations by a different method, and arrived at essentially the same 
conclusions. He sent the results of his computations to a young 
German astronomer named Galle. The latter had the enthusiasm 
and the optimism of youth, and began the search the first night 
after receiving the letter from Leverrier. One can imagine with 
what impatience he waited for the sun to set and the stars to appear. 
When it finally became dark he turned his telescope to the sky and 
found, almost at the place Leverrier had predicted, within half an 
hour after he had begun his search, the unknown world. It is distant 
from the sun nearly 3,000,000,000 miles, and beyond all the senses 
except sight, and then can be observed only with optical aid. It 
had made itself known only through its effects on the motion of the 
planet Uranus, which had accumulated for a period of nearly 70 years. 
It is one of the triumphs of the human intellect that these men 
should have been able, with the instrument of analysis, to penetrate 
to such great distances and find with certainty the existence of a 
world which up to that time had been entirely unknown. 

One might raise the question whether there are not still other 
planets farther out than Neptune. If there are, in the course of 
time they will make themselves felt by the disturbance of the motion 
of the planet Neptune. But since Neptune revolves around the sun 
only once in 165 years, it is clear that a very long time might elapse 
before they both came on the same side of the sun where these 
disturbing effects would be the greatest. Only 66 years have passed 
since the discovery of Neptune, and consequently the chances are 
rather against it having come in conjunction with any other planet 
farther out. At the present time there is no certain evidence of any 
disturbance in the motion of Neptune which can not be explained 
by the action of the planets so far known. On the other hand, 
there is no particular reason to suppose that there may not be other 
planets farther from the sun. 




THE GREAT MOREHOUSE COMET 
Picture taken October 30, 1908 



ASTRONOMY 

PART IV 



COMETS AND METEORS 

Orbits of Comets. Comets are wandering bodies which pass 
around the sun, usually in sensibly parabolic orbits. (See Fig. 67.) 
If their orbits are exactly parabolas it means they have come in 
from the sun from an infinite distance, and will go out again to an 
infinite distance, never to return. It is not possible to say that in 
any case the orbit is exactly a parabola, because the observations 
are made for only a short time while the comet is nearest the sun. 
It is clear from the common sense of the situation that under these 
circumstances the whole extent of the orbit can not be determined 
with perfect accuracy. A very slight error in an observation, which 
would make no sensible difference in the part of the orbit near the 
sun, might make a very great diiference in the remote part. It is 
similar to the problem of determining a circle by means of three 
points. It is known from geometry that if three points not in a 
straight line are given, the circle through them is determined. If 
the three points are very near together the circle is poorly deter- 
mined, especially in the parts remote from the three points. 

While the statement is true that the great majority of comets 
move in sensibly' parabolic orbits, and that it is not certain that 
they move in exactly parabolic orbits, there are certainly some which 
move in elliptical orbits. These comets come in from finite, though 
in some cases great, distances and go out again to the same distances. 
They return to the sun time after time, their periods of revolution 
depending upon the lengths of their orbits. There are a very few 
cases in which it seems that comets move in hyperbolic orbits, 
though there is some room for doubt regarding the conclusion. 

If the comets, as a whole, move in parabolic orbits they can not 
be considered as permanent members of the solar system. On the 
other hand, if their orbits, instead of being parabolas, are very 



186 ASTRONOMY 

elongated ellipses they are permanent members of the system. The 
opinion seems to be growing among astronomers that the comets 
are actually in this sense permanent members of the solar system, 
though no rigorous proof of the statement is at present at hand. 
It has been seen that the orbits of the planets are all nearly in the 
same plane and that the planets revolve around the sun in the same 
direction. In the case of comets it is quite different. Their orbits 
lie in every plane and they revolve in all directions. There is no 
uniformity in their distribution. The only thing that can be said is 
that there is a tendency for the perihelia of comet orbits to cluster 
on the side of the sun which is ahead in its motion through space. 

Dimensions and Masses of Comets. Comets consist of a head 
containing in it, usually, a small bright nucleus, and a long tail 
streaming out in the direction opposite to the sun. The head may 
vary anywhere from 10,000 miles up to more than 1,000,000 miles. 
The nucleus is generally a few hundred, and at the most a few 
thousand, miles in diameter. The tails are in length from a few 
millions up to more than 100,000,000 miles. 

A remarkable thing about the head of a comet is that it nearly 
always contracts as the comet approaches the sun, and expands 
again when it recedes. On the contrary the tail increases enormously 
when the comet approaches the sun, and diminishes as it recedes. 
The nuclei of comets vary in size, but in an irregular fashion for 
which no law has been discovered. 

The fact that the tails of comets point away from the sun is 
a matter of the highest interest. It is not very easy to explain 
precisely the reasons for this. One of the chief hypotheses so far 
advanced for explaining this phenomenon is that the sun exerts an 
electrical repulsion on the particles which come from the head and 
go off in space to form the tail. More recently it has been found 
both theoretically and experimentally that light exerts a pressure 
which depends upon its intensity and upon the surface of the body on 
which it falls. Light pressure is so feeble a force that it does not sen- 
sibly affect masses of large dimensions, but it can be an appreciable 
disturbing influence in very small particles. The general conclusion 
at present is that the tails are produced by electrical disturbances 
and that they project out from the heads of comets in the direction 
opposite to the sun because of electrical repulsion and light pressure. 



ASTRONOMY 187 

Comets shine both by reflected light and by their own intrinsic 
brilliance. When they are far from the sun, i. e., beyond the orbit 
of Mars, they are generally very faint and shine almost entirely by 
reflected light. As they approach the sun they become active 
internally and increase in brightness, not only because they are 
more brightly illuminated by the sun, but also because they become 
self-luminous in some way which is not fully understood. 

Notwithstanding the fact that the volume of a comet is often 
very great, exceeding that of all the planets of the system and even 
that of the sun itself, yet comet masses are very small. This is 
proved by the fact that when they pass near planets, the planets 
pull them entirely from their paths by their attractions, while the 
comets do not in turn disturb the planets enough so that it can be 
observed. In fact, one comet passed through Jupiter's satellite 
system in 1886. This great planet and its satellites totally changed 
the orbit of the comet, but it in turn did not disturb even one of the 
satellites enough so that the changes in its motion could be observed. 
From these facts, chiefly, we infer the very small masses of the 
comets. 

As a comet moves around the sun its mass is continually dis- 
sipated in space along its tail, as is illustrated in Fig. 87. The light, 
volatile materials held in its head and nucleus are evolved under 
the stimulus of the sun's heat and electrical activity, and are repelled 
out into space, never to return to it again. In the case of comets 
which move around the sun in closed orbits, this dissipation of material 
continues until they often become altogether invisible. There are now 
numerous examples of comets whose light has failed, apparently 
because of the dissipation of their luminous parts into space. 

Capture of Comets. Suppose a comet comes into the solar 
system on a very elongated orbit, perhaps a parabola. If it does 
not pass near a planet it will go around the sun and out again on 
a curve of the same character. If it passes near a planet the orbit 
may be entirely changed, and the character of this change depends 
upon the circumstances of the near approach to the planet. Under 
certain circumstances the orbit will be reduced from an elongated 
one to one which is more nearly circular. In this manner a parabolic 
orbit may be reduced to an elliptical one. Jupiter, having a greater 
mass than any other planet and in fact greater than all of them 




Fig. 87. 



Matter Receding from the Head of a Comet and Forming a Long Tail, 
graphed by Barnard 



Photo 



ASTRONOMY 



189 



combined, obviously will capture more comets than any other planet. 
Its chances are favorable also because of its location. If a planet 
beyond Jupiter should capture a comet, this orbit would still pass 
that of Jupiter and Jupiter in turn might capture it and reduce its 
orbit still further. But if Jupiter reduced the orbit of a comet so 
that its aphelion point were at approximately the distance of this 
planet, the planets farther out would thereafter have no sensible 
effect upon it. For these reasons Jupiter has a larger family of 




(Fig. 88. The Orbits of Comets Which Have Been Captured by Jupiter 

captured comets than any other planet. In Fig. 88 the small circle 
represents the orbit of the earth and the large circle the orbit of 
Jupiter. The ellipses are the orbits of those comets which belong to 
Jupiter's family. Some of them have now become invisible because 
of the dissipation of their material in space. 

The planets Uranus and Neptune have small comet families, 
and there are other comets whose aphelia are still farther from the 
sun. Perhaps this may be considered as a reason for suspecting the 
existence of planets farther out than Neptune. The members of 
one small group of comets at their most remote distances, are about 
three times as far from the sun as Neptune is, and the other about 



190 ASTRONOMY 

ten times as far Planets at those distances would revolve around 
the sun in the immense periods of 1,000 and 5,000 years respectively. 

Celebrated Comets. Among the celebrated comets of historical 
times that of 1680 may be mentioned as being the one to which 
Newton's theory of gravitation was first applied. Its orbit was 
computed and it was found that it revolved in a long ellipse with 
a period of about 600 years. At its nearest approach to the sun it 
was only 140,000 miles from the sun's surface, and it moved at the 
rate of 370 miles per second. Its tail, when it was near the sun, was 
100,000,000 miles in length. 

Halley's comet is another one of the important historical comets. 
It appeared in 1682, four years before Newton's publication of the 
law of gravitation. After the work of Newton appeared his friend, 
Edmund Halley, applied his method to the computation of the 
orbit of this comet. He found that it was almost identical with that 
of the comets of 1607 and 1531. He came to the conclusion that 
these various comets were but different appearances of the same 
one, which revolved around the sun in a period of about 75 years, 
there being slight deviations from this number owing to the attrac- 
tions of the planets. Going back in the historical records, it was 
found that comets had been observed at intervals of about 75 years, 
reaching back to a century or so before the beginning of the Chris- 
tian era. There is little doubt that Halley's comet has been observed 
during twenty- five of its approaches to the sun. Halley confidently 
predicted that the comet would reappear and pass its perihelion on 
March 13, 1759. He recognized the fact that the perturbations of the 
planets and the uncertainties in its orbit might make his predictions of 
the time of its next approach to the sun slightly inexact. This was the 
first long range scientific prophecy. It was made in precise mathe- 
matical terms without the use of ambiguous language. The ful- 
fillment or failure of it was awaited with great interest as the time 
drew near. When the year 1759 came the comet reappeared accord- 
ing to the predictions of Halley and passed the sun within a month 
of the time he considered most probable. Before that time there was 
no prophecy in all history made in so definite terms which was so 
literally fulfilled. 

Halley's comet appeared again in 1835, when it passed within 
5,000,000 miles of the earth. Fig. 89 shows the position of the orbit 



ASTRONOMY 



191 



with respect to the earth's orbit and that of Neptune. After its 
appearance in 1835 it went out into space and quickly became invisi- 
ble. For almost 75 years it was beyond the range of even the most 
powerful instruments, and was followed in its course only by mathe- 
matical processes. Though it could not be seen and its existence 
and position could not be proved by any direct processes, yet the 
perfection of astronomical theory is so great that those best qualified 
to judge never doubted for a moment that the theory indicated 
exactly where it was. It was known from the computations that 
it would appear again in 1910. The event is of so recent occurrence 
that everybody knows of its return, and that it passed the sun in 
perfect harmony with the predictions. The newspaper tales of the 
mysteries and peculiarities attached to it were pure fiction. 




.ORBIT DEARTH \S- 
APR 19^ 



I 



Fig. 89. The Orbit of Halley's Comet 

Fig. 90 shows the relative positions of the comet and the earth 
during its time of nearest approach to the sun and the earth. On 
April 19 the comet was at its nearest approach to the sun, but was 
so far from the earth that it was not a very conspicuous object. On 
May 18 it passed between the earth and the sun and at this time was 
visible. Between the latter part of March and May 18 it was visible 
in the morning sky. After May 18 it became visible in the evening 
sky. The diagram, taking into account the direction of the motion 
of the earth and of its rotation, will show the reasons for this. 

Encke's comet, discovered in 1819, is remarkable for the fact 
that it has the shortest known period (3.3 years), and also for the 
fact that its period was shortened during several revolutions without 
any known reason. It has been suggested that it was due to its 
encountering some resisting matter in the system, and that is prob- 
ably the true explanation. 

Biela's comet, discovered in 1826, revolves around the sun in 
a period of 6.6 years and is remarkable particularly for the fact that 



192 



ASTRONOMY 



in 1847 it broke into two parts which gradually separated. Since 
1852 it has not been observed. 

The great comets of 1880 and 1882 were remarkable for their 
splendor, for the nearness of their approach to the sun, and for 
the fact that they moved in almost the same orbit. The orbits of 
these comets are very elongated and their period of revolution, if 
indeed their orbits are elliptical, must be several hundred vears 




- -_ -" £.£.MarAd£i 

Fig. 90. Path of Halley's Comet Showing nearest Approach to Earth 



Consequently, the two objects can not have been the same one. They 
were simply two bodies moving in almost the same paths. Other 
comets moving in the same orbit, at least approximately, were 
those of 1668 and 1843, both of which were brilliant objects. These 
comets either have had a similar origin, or are fragments of a once 
greater comet which has been broken into a number of pieces in some 
transit through the solar system. 

Meteors or Shooting Stars. An attentive watch of the sky on 
almost any clear evening for a little while will show one or more 
so-called shooting stars. They are little flashes of light which have 



ASTRONOMY 193 

the appearance of being a star darting across the sky and disappear- 
ing. Since to call them shooting stars is a little misleading, we shall 
always speak of them as meteors. Instead of being actual stars, 
they are as a matter of fact tiny masses of matter, so small that one 
could hold them in his hand, which are moving in space in the vicinity 
of the earth. Under certain circumstances of motion and position 
they dash into the earth's atmosphere with a velocity which usually 
lies between 10 and 40 miles per second. The heat generated by 
friction with the air of bodies moving with this high speed burns them 
up. The products of their combustion and pulverization fall to the 
earth, or are added to the atmosphere. 

The height of meteors is obtained from observations of them at 
two different places. These observations at the same time give the 
lengths of their luminous paths. If their brightness is also measured 
and the time which they are visible, it is possible to compute the 
whole amount of light which they radiate. This radiant energy 
depends upon the mass of meteorite and its velocity. The velocity 
being known, the mass remains the only unknown and can be com- 
puted. It is in this way that it has been found that the masses of 
meteors are very small, usually being only a few grains. 

The numbers of meteors are much greater than one might 
imagine when he finds that generally he can see only a few in watch- 
ing an hour. The reasons are that he can not see the whole visible 
sky at one time, and that only a small part of the earth's atmosphere 
is within the range of his vision at one time. If a circle is made to 
represent the earth and the atmosphere is put on it to scale, it will- 
be clear why an observer can see so small a part at once. Accurate 
count of the numbers of meteors visible in a given time, made by 
many observers, and computations to extend the numbers so as to 
include all that fall on the whole earth, show that from 10,000,000 
to 20,000,000 strike into the earth's atmosphere daily. 

Meteors strike into the earth's atmosphere from every direc- 
tion, but more are received on the side of the earth which is ahead 
in its motion around the sun than on the side which is behind, for 
the side which is ahead receives not only those which meet the earth 
but also those which the earth overtakes, while the part behind 
receives only those which overtake the earth. It is found that those 
on the side ahead strike with greater velocities than those received 




194 ASTRONOMY 

on the part behind, as would, of course, be expected from the nature 

of the case. 

The part of the earth which is ahead is that which is on the 

morning side of the earth. In Fig. 91 let S represent the sun, E 

the earth, and the arrows the direction 
of rotation and revolution of the earth. 
The point is at the sunrise line and is 
on the side of the earth which is ahead in 
its motion around the sun. 

Relation of Comets and Meteors. As 
the volatile matter which goes to make 
up the tails of comets is dissipated in 
space, there is left behind only the 

Fig. 91. The Earth Encountering x ^ 

Meteors^m it^Re^vohition denser particles which make up the 

head, or perhaps the nucleus. These 
denser particles continue to revolve around the sun indefinitely 
unless the planets disturb their orbits so that they recede to 
infinite distances, which is a possible occurrence, or unless they 
are swept up by the planets. If a planet should strike the remains 
of an extinct comet it would encounter a swarm of particles moving 
in sensibly parallel directions and with equal speed. If these par- 
ticles were small they would produce a meteoric shower. 

Observations show that there are many meteoric showers. 
Particles moving in sensibly parallel lines strike into the atmosphere 
at various times of the year. In some cases the orbits of these 
particles around the sun have been determined. One of the most 
celebrated known cases, and one which has given the most remark- 
able meteoric showers, is that of the meteors which the earth encoun- 
ters on November 14. They move in an elongated orbit of which 
they make the circuit once in 33 years. They have been moving 
so long in the orbit that they are scattered more or less thickly along 
its whole length, but they are more numerous at a certain place 
than elsewhere. Once in 33 years the earth passes through this 
nucleus. The swarm of meteors and the earth move in opposite 
directions, and consequently the earth meets these meteors on its 
morning side. They appear to come out of the constellation Leo, 
and are hence called Leonids. They are almost certainly the remains 
of a comet which was captured by the planet Uranus in 126 A. D. 



ASTRONOMY 195 

This conclusion is based on the computation of the present position 
of their orbit and tracing it back until it was found that at this date 
the meteors and Uranus were very close together, and in such a 
relative position that Uranus would reduce their orbit from a parab- 
ola to an elongated ellipse in which the comet would move in a period 
of 33 years. 

In 1833 the first known remarkable encounter with this swarm 
was experienced. Then, as seen from some places, the sky was filled 
with thousands of meteors. At that time the explanation of a 
meteoric shower was not known. But in 1866, on the same day of 
the same month, a similar meteoric shower was observed. Follow- 
ing this the theory of the phenomenon was fully worked out. 

There are many meteoric showers, though they are on the whole 
less conspicuous than the Leonids. There is a shower visible yearly 
on November 24, in the constellation Andromeda, and other con- 
spicuous ones occur on April 20 and about the 10th of August. It is 
supposed that all these meteoric showers are produced from the 
remains of disintegrated comets. If so, we see how slight the 
masses of the comets are, and how little we should have to fear 
even though one were headed toward the earth and a collision were 
certain. 

Influences of Meteors on the Earth. It might be supposed 
that objects so small as meteors would have no sensible effect on a 
great body like the earth, and such is the case if only a short period 
of time is under consideration. But in astronomical and geological 
science the earth is considered not only for years and centuries, but 
for millions of years. Though the effects of meteors are insensible 
for years or even centuries, it may be that in the long run they are 
very important. Sometimes those influences which, though small, 
work continually in one direction are the most important. For 
example, the washing down of mountains and hills and plateaus 
by running water is not a matter of any consequence for a short 
time, but when considered during the vast ages of the geological 
changes this is one of the most important agencies in transforming 
the earth. 

One effect of meteoric matter circulating around the sun is to 
resist the motion of the earth a little. This resistance has a slight 
tendency to decrease the size of its orbit and to bring it nearer and 



196 ASTRONOMY 

nearer to the sun. In a similar manner the resistance also slightly 
retards the rotation of the earth and thus makes the day longer. 

Another effect of the sweeping up of meteoric matter by the 
earth is that the earth's mass in this manner continually grows. It 
is conceivable that the earth has been revolving around the sun 
long enough to make this a very important factor in its evolution, 
and it is also conceivable that in former times the rate at which 
meteoric matter was acquired was much faster than at the present 
time. An indirect effect of the growth of the earth is that because 
of its greater gravitative power it slowly though slightly winds in 
toward the sun. Xo calculations are at hand which enable us to 
give any precise estimate of the effects of these causes upon the 
evolution of the earth. 

Meteorites. Xow and then large bodies, weighing from a few 
pounds up to a few tons, dash into our atmosphere and plunge down 
through it in a few seconds and strike the surface of the earth with 
great violence. Those bodies whose masses are so great and which 
are solid enough to last until they strike the surface of the earth, 
are called meteorites in contrast to those which are burned up in the 
atmosphere and which are known as meteors. The meteorites are 
generally composed largely of rocky material, though they are often 
mixed with some metallic iron. "When pure iron is not found its 
compounds are usually present. About three or four per cent of 
the meteorites which fall are almost pure iron mixed with a little 
nickel. Altogether about thirty of the eighty elements known on 
the earth have been found in meteorites, but no new substances. 
Yet the structure of meteorites is quite different in some cases from 
that of any minerals found on the earth, and from an examination 
of them it can be proved that they are of extra-terrestrial origin. 

Some meteorites show evidences of remarkably perfect crystal- 
lization; others show places where they have sometime been frac- 
tured and later cemented. Sometimes at the fractured place one 
part has slipped slightly on another before they were again joined 
in a solid mass. These facts are very important in connection with 
theories regarding their origin. The very perfect crystallization, 
as well as the fractures and re-cementation, indicate strongly that 
these bodies are fragments of large masses of world-like dimensions. 
If so, they are not masses ejected from the sun or by volcanoes from 



ASTRONOMY 197 

the earth and moon, for in those cases they would cool quickly and 
be glassy rather than crystalline, and there would be no chance for 
fractures and re-cementation. Chamberlin has suggested that 
probably they are fragments of planets which once existed before 
the origin of our present system. 

THE SUN 

Light and Heat Received from the Sun. It is a matter of com- 
mon observation that the sun furnishes the earth an enormous 
amount of light. Compared to full sunlight, almost any artificial 
light used for illumination seems dull and feeble. Even when the 
sun's rays are largely cut off by clouds, the illumination of a room 
or building is generally much greater than it is at night with the 
artificial lights which are ordinarily used. A direct measurement of 
the intensity of sunlight shows that it is 60,000 times that of a 
standard candle at a distance of one yard. 

Light is a wave motion in the ether in many respects similar 
to sound waves in the air, though there are some fundamental differ- 
ences. Sound waves to which the ear is sensitive vary in length 
from approximately an inch to many feet. Light waves to which 
the eye is sensitive vary in length from about -g-g-.Vo-TT of an inch for 
the red to about ts-.Vtj o of an inch for the violet. The longest waves 
are less than twice as long as the shortest ones. In the terminology 
of acoustics, our eyes are sensitive to less than one octave of light 
while our ears are sensitive to ten octaves of sound. There are vibra- 
tions in the ether shorter than violet rays and others much longer. 
Those which are shorter than the violet rays are known as the ultra- 
violet, or chemical, rays, and those which are longer than the red 
rays are known as the infra-red, or heat, rays. From the standpoint 
of physics all of these rays are similar, and for short we may term 
them altogether radiant energy. The heat waves raise the tem- 
perature of a dark object on which they fall, and so also do both the 
light waves and the chemical waves. It follows that in considering 
the light and heat received from the sun we may group all of it 
together and treat it as a single type of energy. 

It is possible to measure directly the radiant energy received 
from the sun at the earth's surface. The difficulty in measuring 



198 ASTRONOMY 

how much is actually received by the earth arises from the fact that 
it is hard to determine how much is absorbed in passing through the 
atmosphere. But by making observations at the sea level and again 
on high mountains, and taking into account the difference in the 
amount of air which the energy has passed through at the two posi- 
tions, it is possible to get a tolerably accurate estimate of the absorb- 
ing effects of the atmosphere. In describing the energy received 
from the sun we may express the quantity in various units, as for 
example, the calory used by engineers, or the horse-power, which is 
in more common use. Everyone is familiar with the fact that heat 
energy is equivalent to work, and an example of its transformation is 
in the steam engine where the heat, generating steam, does work by 
means of the steam engine. The unit of work known as the horse- 
power will raise 33,000 pounds one foot high in one minute. Obser- 
vations show that the radiant energy received from the sun on every 
square yard exposed perpendicularly to its rays is equivalent to 
three horse-power. The earth's surface is four times the area of a 
circle whose diameter is equal to that of the earth, and consequently 
the average amount of energy received per square yard on the whole 
earth's surface is three-fourths of a horse-power. It follows from 
this that, if the energy which falls from the sun on a manufactory 
could be used for mechanical purposes, it would run all the machin- 
ery within it. But it is not possible to use more than a very small 
fraction of the sun's energy for the purpose of doing work. 

Notwithstanding the fact that the sun's energy is not directly 
available as a source of power, it is worthy of note that almost all the 
energy which we use has been derived indirectly from the sun. A 
former important source of energy was the wind which drove thou- 
sands and thousands of windmills, and pushed boats over the seas. 
The energy of the winds is entirely due to the sun. The winds blow 
because the sun heats up the equatorial zone of the earth more than 
it does the higher latitudes. 

Another source of energy which was formerly more important 
relatively than it is at present, was the water power. The energy given 
up by the waterfall was indirectly derived from the sun; the sun's 
heat raised the water in the form of vapor from the oceans and lower 
levels into the atmosphere, and the winds carried it in many cases 
thousands of miles out over the land where it fell as rain or snow on 



ASTRONOMY 199 

the mountains and in the higher altitudes. Running down from 
the higher places and uniting into rivers, it became a practical 
source of energy where it plunged over precipices. The original rain 
may have fallen from an altitude of a half-mile or a mile, while in 
the waterfall we generally use a fall of not many feet, and in extreme 
cases not more than a hundred or so. It is obvious from this how 
small 'a fraction of the energy of the falling water could be utilized 
even if every waterfall in the world were used to the extreme limit. 

The amount of energy in the falling water can be seen from 
the number of tons which descend in a heavy rain. While an inch of 
water is a very heavy rain, yet this amount often falls in a few hours. 
Since the weight of a cubic foot of water is 62J pounds, a little com- 
putation shows that, in an inch of rain on a square mile, more than 
60,000 tons fall from the sky to the earth. In a large part of the 
United States the annual rainfall is about 30 inches, or in round 
numbers 2,000,000 tons per square mile. Remembering that in 
North America alone there is a territory of at least 1,500 miles square 
where the average rainfall is about 2,000,000 tons per square mile, 
one gets an idea of the enormous energy the sun has put forth in 
evaporating the water of the oceans and raising it into the air. 
Clearly, this is an extremely small fracti6n of the solar energy which 
falls on the earth. 

The most important source of energy at the present time for 
mechanical purposes is undoubtedly coal. The coal had its origin 
in plant life which flourished ages ago. Consequently, the energy 
which the coal gives off when consumed in our furnaces, was origi- 
nally derived from plants. Now, the plants get their energy from 
the sun. The little cells in the leaves and stems are minute labora- 
tories where the sun does work and where its energy is stored up. It 
is, of course, true that the plants live to some extent on the earth and 
water, but an examination of their constitution shows that it is a 
fact that almost all the energy which is stored up in their fibers has 
been derived from the sun. Consequently, when one sees a rail- 
way train driven by the coal which is fed into its furnace, he is seeing 
it pushed indirectly by energy derived from the sun. It follows 
from the fact that the plants receive their energy almost entirely 
from the sun that the animals, which live upon plants, receive their 
energy almost entirely from the sun. As a matter of fact, almost all 



200 ASTRONOMY 

the motions and activities which come under our observation, except 
the motions of the heavenly bodies themselves, are due to energy 
derived from the sun. 

The earth, as seen from the sun, would be a very small point in 
the sky, about as large as Mars appears from the earth. The sun 
radiates heat and light into space in every direction. Consequently 
it follows that the amount of light and heat received by the earth 
from the sun is only a very small fraction of the whole amount 
radiated. It is approximately T.innr.iruT.oTo' of the energy poured 
out by the sun. This means that the sun's surface is radiating heat 
and light at an enormous rate. The computation shows that on the 
average 140,000 horse-power are continuously radiated from every 
square yard of the sun's surface. In order to generate this enor- 
mous energy a layer of anthracite coal 25 feet thick would have to 
be consumed every hour. Xo blast furnace so far devised could 
develop energy at this enormous rate. Expressed in other terms 
the heat of the sun would melt a layer of ice 4,000 feet thick every 
hour over its whole surface. 

It is a certain inference from the great rate at which the sun 
radiates heat that its temperature is very high. It is not easy to 
measure the exact temperature, first, because it is higher than can 
be produced upon the earth, and second, because there is no one layer 
of the sun which alone radiates light and heat. The high layers 
radiate vast quantities and in turn absorb much from the lower lay- 
ers, which are also radiating. The higher layers are undoubtedly 
of somewhat lower temperature than the lower layers. But all 
recent determinations agree in showing that the temperature of 
that part of the sun which radiates light and heat into space is in 
the neighborhood of 10,000° F. This is several thousand degrees 
above the highest temperature so far obtained in the most powerful 
electrical furnace, and is sufficient not only to melt but also to vola- 
tilize all substances known on the earth. 

Source of the Sun's Heat. Since the sun is pouring out an 
enormous quantity of energy into space, it would cool off in the 
course of time unless its heat were in some way replenished. Of 
course, since it is a very large body it would not cool off quickly. 
And the rate at which a body cools off depends not only on its size 
and mass but also upon its constitution. For example, a rock of a 



ASTRONOMY 201 

given weight will cool off more quickly than the same weight of 
water; or expressed otherwise, it takes more heat to raise the tempera- 
ture of a given weight of water than it does to raise the temperature 
of the same weight of rock to an equal degree. In fact, more heat 
is required to raise the temperature of a given mass of water a cer- 
tain number of degrees than of almost any other known substance. 
Now, if we assume that the sun cools off as slowly as water, we can 
compute how fast its temperature will fall since we know how fast 
it radiates heat. The computation shows that if the sun's heat were 
not kept up by some process, its temperature would fall about four 
degrees per year. Consequently in 3,000 years it would become cold. 
This proves that in some way the sun's heat is continually being 
restored. 

We are accustomed to associating heat with fire, and it seems 
perfectly natural to imagine that the sun is a great place of confla- 
gration, or a sort of furnace. Now, the combustion of a definite 
quantity of coal produces a definite quantity of heat, and it is easy 
to see that one can calculate how long the heat of the sun would be 
maintained if it were made of pure coal and oxygen, and if the heat 
were due entirely to the burning of the coal. It is found on making 
the calculations that, according to this theory, the heat of the sun 
would be maintained only about 1,000 years. The theory is clearly 
inadequate to account for the facts. 

iVbout 1850 a new principle in physical science, known as the 
conservation of energy, was developed. In brief it is that the total 
amount of energy in the universe does not change. It may change 
its form but not its quantity. For example, if a body is in motion 
it has a certain amount of energy called kinetic energy. If it strikes 
something and is stopped its kinetic energy is destroyed, but it is 
found that in place of the kinetic energy its temperature has been 
raised by the impact. Also some energy has been given forth as 
sound. But neglecting the sound and all the energy except that 
which is manifested in the increased temperature of the body, it is 
found that its increase in temperature is exactly equivalent to the 
kinetic energy it had, and that it can be transformed again into 
kinetic energy. It has been found that a body falling, subject to 
the earth's gravity, 772 feet has so much energy of motion when it 
strikes that its temperature is raised 1° C. 



202 ASTRONOMY 

Following out the idea of falling bodies, it was suggested about 
1850 that the sun's heat might be due to the impact of meteors fall- 
ing in upon it. Because of the great gravitative power of the sun, 
a meteor would strike its surface with a velocity of about 480 miles 
per second. The quantity of heat generated by a body striking the 
sun at such an enormous velocity would be thousands of times that 
produced by the combustion of any mass of equal weight. But when 
the computations were made to determine the quantity of meteoric 
matter which would be required to keep up the enormous radiation 
of the sun, it was found that it was so great that in its passage among 
the planets it would not only seriously disturb their motions, but 
would sensibly raise the temperatures of the planets themselves by 
striking in upon them. If this meteoric matter came from space 
beyond the planets it would produce on the earth about ^tt as much 
energy as is received from the sun. Since this is millions of times 
as much energy as we receive from the meteors, obviously the theory 
is not quantitatively sound. 

Almost at the time of the development of the meteoric theory 
a very remarkable contribution was made to the subject by the great 
German physicist, Helmholtz. He saw that if the sun were slowly 
contracting, the contraction would elevate the temperature of the 
sun and restore its heat. A contraction of a body is equivalent to 
a small fall of all of its particles towards its center. While at first 
thought one might suppose this would be quantitatively insufficient, 
yet the computation shows that, because of the enormous volume of 
the sun, an annual contraction of about 180 feet in the sun's radius 
would account for all the heat and light it radiates. So small a con- 
traction on so large and distant an object as the sun would not become 
visible with even our best instruments until it had continued more 
than 6,000 years. In 1870, Lane showed that a gaseous body radiat- 
ing heat into space would necessarily contract, and that in contract- 
ing its heat would not only be restored but its temperature would 
actually rise so long as it remained gaseous. 

According to the contraction theory, which is quantitatively very 
much more satisfactory than any earlier one, the sun was larger in 
the past than it is at present, and in the future it will become 
continually smaller. This enables us to compute how long the sun 
can have radiated light and heat sensibly at its present rate. In 



ASTRONOMY 203 

making the computation for its effects on the earth, we do not need 
to follow it back beyond the time when it extended out to the earth. 
The computation shows that if the contraction theory is correct, and 
if the shrinking of the sun is the only source of its energy, then it 
can not have radiated light and heat on the earth at its present rate 
more than about 20,000,000 years. If this is the whole story, the 
series of changes through which the earth has passed and the evolu- 
tion of. plants and animals which live upon it have taken place 
inside of 20,000,000 years. Turning to the future, we can calculate 
how long it will be before the density of the sun will become so 
great that further contraction will be impossible. Assuming that it 
will not contract further when it gets as dense as iron, it follows 
that the future existence of the sun as an efficient source of light and 
heat will extend over only 8,000,000 or 10,000,000 years. 

The contraction theory of the heat of the sun certainly is sound, 
and until recently was supposed to be the only source of the sun's 
energy. On the basis of the computations just mentioned, physicists 
and astronomers made rather definite statements of the age of the 
earth and the period during which evolution on its surface could 
have taken place. The geologists and the zoologists on the basis of 
data in their own sciences came to the conclusion that the earth 
has been undergoing an evolution much longer than 20,000,000 years. 
They were by no means in harmony on the matter, for their esti- 
mates ranged all the way from 50,000,000 to 500,000,000 years. 
Recently we have found reasons for believing that perhaps there are 
other important sources of heat in the sun. Since the discovery of 
X-rays and radium it has been found that certain kinds of matter 
undergo disintegration. That is, certain large molecules such as 
those of radium and uranium break up into molecules of smaller 
weight, and in the process of disintegration give forth enormous 
quantities of energy. The amount of energy is of the order of 1,000,- 
000 times that produced in the combustion of equal weights of any 
known substance. One of the products of disintegration of radium 
is helium. Now radium is not certainly known to exist in the sun, 
but helium is extremely abundant there. In fact, helium was first 
known in the sun, and its name comes from the Greek word for sun. 
The fact that helium is abundant in the sun, perhaps can be inter- 
preted as indicating that radium is there and has been undergoing 



204 ASTRONOMY 

disintegration. It is certainly possible, therefore, and indeed probable, 
that an important source of the sun's energy is the disintegration of 
matter. It is well within the bounds of possibility that this is the 
most important source of its energy. At the present time there is 
no reason to conclude that the sun has radiated light and heat at 
its present rate for only 20,000,000 years. The period may just as 
well be 10 or 50 times as long. Similarly, there is now no reason to 
suppose that in 8,000,000 or 10,000,000 years in the future its light 
will begin to fail. While no positive statements can be made regard- 
ing the matter, it does not seem, in the light of our present knowl- 
edge, unreasonable to suppose that the future existence of the sun and 
earth in approximately their present states will extend over many 
hundreds of millions of years. 

Sun Spots. The most conspicuous markings ever observed upon 
the sun are relatively dark spots which frequently appear in its 
luminous surface and last from a few days to a few months. The 
opaque, extremely luminous surface of the sun is called the photo- 
sphere. The sun spots are phenomena of the atmosphere. They are 
composed of a dark nucleus, called the umbra, which is surrounded 
by a somewhat lighter band, called the penumbra. The penumbra 
often is composed of a series of filaments reaching from the light 
photosphere into the umbra. The spots have been spoken of as 
being dark. This statement is slightly misleading, for they are only 
relatively dark with respect to the intensely luminous photosphere. 
The actual umbrae of the spots are as bright as the most intense 
artificial light we have. 

The diameters of the spots may be anywhere from 500 to 50,000 
miles, and some penumbrae reach up to 200,000 miles. Often a 
single penumbra may contain many umbrae in its interior. The 
development of a sun spot is usually preceded by indications of 
violent disturbance in its region, and bright points with intervening 
dark places are generally observed immediately before the appear- 
ance of a spot. The dark places unite and form a spot after an 
interval of a few hours or in some cases a few days. 

The sun spots have the appearance of being dark holes in the 
surface of the sun. We unconsciously draw this conclusion because 
our experience on the earth tells us that holes into its interior, such 
as tunnels and the mouths of mines, appear dark. If our experience 



ASTRONOMY 205 

had been the opposite, then undoubtedly a dark spot on a distant 
world would appear as a mountain to us instead of a hole into its 
interior. Such a conclusion would be more nearly correct in the 
case of the sun spots. Instead of being dark openings into the 
interior of the sun they are masses of cooler gas which are usually 




Fig. 92. Photograph of the Sun Showing Spots on Its Surface 

above the general surface of the sun's photosphere. (See Fig. 92.) 
This is proved by the fact that as they appear near the margin of 
the sun they are relatively more conspicuous than they are at the 
center of its disk. Fig. 92 is a direct photograph of the whole disk 
of the sun showing several spots and the absorption near its margin. 
The number of sun spots varies greatly from year to year and 
they are not uniformly distributed on the sun. They occur in greater 



206 ASTRONOMY 

numbers for a few years and then are less numerous, running through 
the cycle of changes in about 11 years. They appear in greatest 
numbers in belts on each side of the sun's equator. When they 
begin to become more numerous, they appear first in greatest num- 
bers at latitudes about 35 degrees north and south of the equator. 
As time goes on they appear most frequently in lower and lower 
latitudes, reaching their greatest numbers when they are at about 
20 degrees north and south of the equator. Then they begin to 
diminish in number and size and disappear at latitudes approxi- 
mately 6 degrees north and south. At the same time a new series 
begins in the higher latitudes. 

From the observations of sun spots it has been possible to 
determine the rate of rotation of the sun. Considered as a whole, 
its period of rotation is about 26 days, and its motion is in the 
same direction as that of the revolution of the planets around it. 
The sun does not rotate as a solid, but its equatorial zone moves 
faster than those parts in higher latitudes. The equator rotates in 
a period of about 25 days, spots in latitude 30 degrees complete their 
revolution in about 26| days, and those in latitude 45 degrees in 
about 27 days. Spots are not seen in latitudes higher than 45 
degrees. The rotation of the sun has been determined in several 
other ways, principally by observations of bright spots and great 
elevations which the spectroscope shows, and there is in a general 
way agreement of these results with those obtained by the obser- 
vations of spots. 

Different Layers of the Sun. The lowest layer in the sun 
which we can see is the photosphere, mentioned above. It is the 
opaque, apparently solid or liquid surface of the sun. Certainly, 
instead of being in a solid or liquid state, it is almost entirely gaseous 
because of the sun's high temperature. It is largely composed of the 
ordinary terrestrial elements in a gaseous state, and has the appear- 
ance of being a continuous surface because of the immense numbers 
of small liquid particles of carbon, rock material, and iron floating 
in it. It is somewhat analogous to clouds in our atmosphere. A 
cloud appears to be an opaque solid substance when seen at a dis- 
tance, but as a matter of fact it is almost entirely gaseous. It gets 
its appearance from great numbers of minute particles of water 
floating in the atmosphere. 







!«#" '-.«*; <-,.v*"v; 






'. - • • , 



^ v.. ■■.•-.■•• -v 



r '.-...■ - V 





Fig. 93. The Sun's Photosphere Highly Magnified 



208 



ASTRONOMY 



In Fig. 93 is shown a small portion of the photosphere highly 
magnified. It is seen to be composed of a large number of minute 
granules with darker places between. The light spots are the tops 
of ascending currents which are bringing the heated material up 
from the interior to restore that lost by radiation; the darker places 




Fig. 94. Eruptions from the Sun Photographed at the Yerkes Observatory by Fox 



are where the partially cooled gases are sinking back into the depths. 
These bright spots are generally from 500 to 1,000 miles in diameter. 
Above the photosphere lies a less intensely heated atmosphere, 
called the reversing layer, which contains at least about half of our 
terrestrial elements, all in the gaseous state. Among these elements 
are a large fraction of the metals with which we are familiar. The 
thickness of the reversing layer averages about 500 or 600 miles. 



ASTRONOMY 209 

Mixed throughout it and possibly to some extent below it, is a thin 
cloud of small liquid or solid particles. The effect of this cloud is to 
absorb some of the light radiated by the photosphere and to reduce 
its intensity, particularly near the margin, as is shown in Fig. 92. 
Above the reversing layer is what is called the chromosphere (color 
sphere). This is a gaseous envelope of 5,000 to 10,000 miles in 




Fig. 95. The Sun's Corona Photographed at the Time of a Total Eclipse of the Sun 
in 1900 

depth. At the time of total eclipse it can be seen as a scarlet ring 
surrounding the entire sun, whose surface seems to be seething with 
tongues of leaping flames. The spectroscope shows that the chromo- 
sphere is made up of luminous hydrogen, helium, and calcium. 

The photosphere seems to be relatively quiet and continuous 
except where it is broken up by the spots. On the other hand, the 



210 ASTRONOMY 

chromosphere is the seat of numerous disturbances. Vast eruptions, 
called 'prominences, rise up from it to altitudes of from 50,000 to 
300,000 miles with velocities sometimes as great as 500 miles per 
second. Fig. 94 is a photograph of some of these remarkable streams 
of material. On the sun explosions frequently take place in which 
masses of matter, whose volumes are greater than that of the earth, 
are thrown aloft to a distance farther than from the earth to the 
moon. This material, which rises in prominences, goes up and often 
turns over in long graceful streamers similar to the path of a sky- 
rocket, and plunges back again upon the sun. 

Outside of the chromosphere is the corona, a vast envelope 
surrounding the sun and reaching out to 500,000 or 1,000,000 miles 
from it. The corona can be observed only at the time of total eclipse 
because it is so faint that the illumination of our atmosphere entirely 
obscures it. It has some of the properties of an .atmosphere, and 
some which are considerably different. It does not uniformly sur- 
round the sun but stretches out farthest in the plane of its equator. 
Its shape varies from time to time with the period of the sun spot 
activities, and is undoubtedly associated with the disturbances on 
the sun's surface. Around the poles of the sun it is arranged in 
streaks, showing that strong magnetic forces are at play there. 

Fig. 95 shows a photograph of the corona at the time of a total 
eclipse in 1900. 

Spectrum Analysis. When substances are in the gaseous state 
and luminous, they give forth vibrations whose character depends 
upon their chemical constitution. The vibrations are distinguished 
from one another chiefly by their frequency, or the number given 
out per second. For example, incandescent hydrogen gives vibrations 
of a certain frequency, and incandescent oxygen gives vibrations of 
quite a different frequency, and so on for all the elements. The 
different light radiations from different elements are somewhat 
analogous to the different sound vibrations given forth by different 
kinds of bells, the pitch depending upon the number of sound waves 
given out per second. The reason that the matter must be in the 
gaseous state in order to get its characteristic speetrum, is that 
when it is in the solid or liquid state, the vibrations of the parts of 
the molecules which produce the light waves are interfered with by 
their being restrained by the neighboring molecules, and are there- 



ASTRONOMY 



211 



fore, not free to vibrate with their normal frequency. But when 
matter is in the gaseous state, as was explained in connection with 
the atmosphere, the molecules are independent of one another, ex- 
cept for brief times during collisions, and the normal oscillations 
take place unhampered. Consequently, the character of the vibra- 
tions of the molecules depends simply upon their structure. It is 
clear from this that if some means can be devised of discovering the 
character of the vibrations coming from a luminous gas, its nature 
can be determined in this fashion. The spectroscope is an instru- 
ment precisely for this purpose. 

Fig. 96 shows the principles upon which spectrum analysis 
depends, though an instrument for practical use is modified so as 




Fig. 96. Diagram Showing the Dispersion of Light Which Passes Through a Prism. 
Dispersion is at the Basis of Spectrum Analysis 

to get a brighter spectrum. Let L be a dense beam of parallel rays 
of white light which fall on the screen S, at 0. Suppose is a narrow 
opening of the slit through S lt which may be from tJ-q toyVoir of an 
inch wide. A thin slice of light passes through and falls on the 
prism P. It strikes the first surface of P obliquely and its direction 
is bent as it enters it. The direction of the light is not only bent, 
but the light is spread out into its different colors. When the light 
emerges from P it is bent still farther and spread out still more. It 
may be caught upon the screen S 2 , when it will be found that it 
consists of a band of colors varying from the violet v on the end 
which is bent the more, to the red r on the other end. The violet 
rays are the shortest (that is, the rays with the greatest frequency) 
which are visible to the human eye, and the red are the longest. 



212 ASTRONOMY 

Beyond the violet there are the chemical rays and beyond the red 
in the other direction the heat rays. 

Now, suppose a single substance in the gaseous state is heated 
to incandescence. For example, let us consider sodium, which is the 
metal constituent of ordinary salt. The light will appear to the eye 
as yellow and when it passes through the prism and falls on the 
screen S 2 , there will be seen light at two places near together in the 
yellow. That is, sodium in the incandescent gaseous state gives forth 
vibrations of two different frequencies which are so near together 
that they both are yellow light. It is found by experiment in the 
laboratory that sodium always gives these two kinds of yellow light, 
and that no other substance gives exactly the same kinds of light. 
It must be understood that the actual instruments in use are much 
more powerful and give a much brighter spectrum than that indi- 
cated in the simple sketch of Fig. 96. Now, suppose iron is made 
incandescent and that it is in the gaseous state. When its light is 
passed through the prism P and falls on the screen S 2 , it will be 
found that there are bright lines at very many places. The iron 
molecule seems to be extremely complex and gives forth many kinds 
of vibrations, but the important fact in this connection is that it 
always gives the same vibrations and it gives no vibrations which 
are emitted by any other substance whatever. 

Now, suppose that the light instead of coming from a point in 
the laboratory comes from the distant sun, or even from the much 
more distant stars. The character of its vibrations will not have 
been changed in its journey through space any more than the char- 
acter of the vibrations from a musical instrument will be changed by 
passing some distance through the air; the tune is the same whether 
the instrument is near to us or far from us. It follows that if the 
distant object is an incandescent gas its light will be analyzed into 
its separate parts and will fall on the screen S 2 a "t distant places, 
depending upon the constitution of the gas. If the substance is one 
with which we have become familiar in our laboratories we shall 
recognize its presence by the character of its light when analyzed. 
In fact, if the source of light is composed of a mixture of many 
substances the presence of all of them can be determined, for though 
originally it is a mixture of various colors the spectroscope will sepa- 
rate them into their constituent parts and each one will be distinct 



ASTRONOMY 213 

from every other. For example, if there were a mixture of sodium 
and iron the yellow lines of sodium would appear in the spectrum, 
and also the numerous lines of the iron. When the light is thus 
analyzed into its separate parts, the presence of one kind of lines 
does not interfere with the detection of any other kind. It is clear, 
therefore, from all of this discussion that the chemical constitution 
of an incandescent gas can be determined by means of the spectro- 
scope, however far away it is in space. This remarkable process has 
been understood for about 50 years. Before its discovery it was 
supposed that while we can determine the motions of the heavenly 
bodies and in most cases their masses and dimensions, nevertheless, 
their constitution was a field forever closed to us. 

There is another phase to spectrum analysis which in application 
is often more important than the preceding results. Suppose the 
light L is white; that is, that it comes from an incandescent solid 
or liquid. Then, as has just been explained, its spectrum will be 
continuous, and the substance of which it is composed can not be 
determined. But suppose that between S 1 and P there is interposed 
a cooler gas. This does not mean by any means that it shall be cold, 
but simply that it shall be less luminous than the source of the 
light L. This cooler gas will absorb some of the light L, and the 
important fact is that it absorbs precisely those vibrations which it 
would itself give out if it were incandescent. For example, suppose 
the cooler gas between S x and P is sodium. Then the spectrum on 
$2, instead of being a continuous band of light from the violet to 
the red, will be a continuous band, except where it is crossed by 
two dark lines in the yellow at precisely the place where the yellow 
bands of sodium fall. That is, the interposed sodium gas has been 
transparent to all the colors except those which it itself radiates. 
This absorption by a gas of the same colors it radiates is analogous 
to the fact that a musical instrument, for example a piano, will take 
up those same vibrations when produced on another instrument that 
it is capable of giving forth. If middle C on one piano is struck and 
the key of middle C held down on a neighboring one, the second one 
will be set vibrating by the first, but if D be held down on the second 
one no sensible vibrations will be induced. 

It follows from these principles that if the source of light is an 
incandescent solid, and if a cooler gas is between it and the observer, 



214 



ASTRONOMY 





1 


1 ■ ■- -. 4 


" 




■£" 


...: -'•: 


~- 





Fig. 97. 
Solar 

T 



A Portion of the 
Spectrum on a 
,arge Scale 



he can determine the chemical constitution of 
the interposed cooler gas but not of the actual 
source of light. Let us apply these results to 
the sun. The photosphere is the main source 
of light in it and, as has been explained, the 
photosphere owes its intense luminosity and 
opaque appearance to the fact that it is made 
up of small drops of liquid particles of carbon, 
iron, rock material, etc. The light from this 
photosphere passes through the cooler gaseous 
envelope above it, called the reversing layer. 
The reversing layer subtracts from the light of 
the photosphere certain rays and produces 
many dark lines in the sun's spectrum, which 
would otherwise be continuous. Fig. 97 shows 
a small part of the solar spectrum; the left 
part is the spectrum of the photosphere and 
the right that of a spot. With the powerful 
modern instruments 20,000 lines can be 
observed in the spectrum of the sun. So far 
about 12,000 of these lines have been meas- 
ured. While not all of them have been iden- 
tified with terrestrial substances, about half of 
the elements known to the earth have been 
found to exist in the sun. Among the more 
common ones we may mention hydrogen, 
helium, carbon, oxygen, sodium, magnesium, 
aluminum, silicon, potassium, calcium, iron, 
nickel, copper, zinc, silver, tin, and lead. The 
state of the sun can be imagined when it is 
found that in its cooler atmosphere all of these 
elements are in a gaseous condition. 

Another very interesting application of the 
spectroscope has been made in the photography 
of the sun. In the case of certain lines, the 
vapors which surround the photosphere are 
so extensive and so dense that they cut out 
nearly all the light which comes from it, but 



ASTRONOMY 



215 



above these vapors there are floating luminous clouds of the 
same material. The width of an absorption line increases with the 
density of the absorbing medium. In the case under consideration 
the lines are wide because of the density of the absorbing gases which 
are subject to great pressure. The higher luminous gases are subject 
to less pressure and give, therefore, a bright line in the center of 
the dark absorption line. That is, in the sun's spectrum in the case 
of some wide heavy lines there are bright centers. The light in 
these centers comes from definite elements. When the sun's light is 




Fig. 98. Photographs of Spots Taken with Calcium Light 



spread out into a spectrum so that the light from each incandescent 
substance comes out in a different place, it may all be screened off 
except that which comes from a single substance, If a photograph 
is taken, a picture of the sun is obtained with the light which comes 
from a single element. In order to obtain a photograph of the whole 
sun it is necessary to have the apparatus adjusted so that the 
photographic plate will move at the same time the spectroscope is 
pointed at different parts of the sun, for otherwise the images of 
different parts would fall upon the same part of the photographic 
plate, and we should obtain a composite picture rather than a picture 



216 ASTRONOMY 

of its whole surface. When the instrument is properly adjusted, a 
photograph of the whole sun in light from one element is obtained, 
and the picture shows distribution of this element in the sun at the 
time in question. This instrument is called the spectroheliograph. 

Figs. 98 and 99 are spectroheliograms of the sun. Fig. 98 
shows a small portion of the solar disk including some spots as 
photographed with calcium light, and Fig. 99 shows the same region 
as photographed with hydrogen light. The luminous places are 
where the element in question Avas abundant in an incandescent 



Fig. 99. Photograph of the Same Spots as Shown in Fig. 98 Taken with Hydrogen Light 

state. The relatively dark places are where the element was present, 
but in such a cool condition that it absorbed almost completely the 
light from the photosphere. 

THE SIDEREAL SYSTEM 
Distribution of Stars. In connection with the work on constel- 
lations we saw that stars were apparently grouped in various parts 
of the sky. This apparent aggregation here and there depends, of 
course, upon our position with respect to them. At present we are 
not interested in their apparent grouping, but in their actual distri- 
bution in space. This is, of course, related somewhat to their apparent 



ASTRONOMY 217 

distribution; or, at least, their apparent distribution depends partly 
upon their actual distribution. 

An examination, either without a telescope or with a telescope, 
shows that the stars are much more numerous in the direction of 
the Milky Way than they are in directions at right angles to it. If 
a given area be counted in the plane of the Milky Way and an equal 
area be counted at right angles from it, it will be found, especially 
if very faint stars are included, that the region in the Milky Way 
has many times more stars than the other one. It follows that stars 
are either more closely crowded together in the direction of the 
Milky Way, or that in those directions we are looking through a 
greater depth of them. That is, appearances have led to the conclu- 
sion that the system of the stars is a great disk or grindstone-shaped 
figure in space. The sun and its family of planets is somewhere in 
the interior of this vast aggregation of stars. The plane of the disk 
is the plane of the Milky Way. When we look out in the direction of 
the Milky Way we see a vast aggregation of stars because we are 
looking through a greater depth of them; and when we look out at 
right angles to it we see fewer stars because we are looking in a 
direction where w T e sooner reach the borders of the system. 

The fact that photographs of the Milky Way show dark rifts 
and breaks, as in Fig. 37, is against this theory without some con- 
siderable modifications. Recent studies of the apparent motions 
of the stars show that those so far examined, which, of course, do 
not include the great majority of those stars which are extremely 
faint, belong, on the whole, to two great star streams. Probably 
the sidereal system is made up of a relatively small number of great 
star families, the numbers of which move in parallel lines with 
approximately the same speed. 

Most of the stars are so remote from us that their distances 
can not be found by direct processes. One of the proofs of the earth's 
revolution around the sun is the parallax that certain stars are 
observed to have. (See Fig. 20.) But parallaxes of a sufficient num- 
ber of stars can not be obtained by this method to give any general 
idea of their distances when considered as a whole. There are, how- 
ever, certain indirect processes which have led to most interesting 
results. If the stars were still and the sun in motion, they would 
apparently drift back in the direction opposite to that of the motion 



218 ASTRONOMY 

of the sun. The apparent rate at which they would drift back would 
depend upon their distance from the sun. It is analogous to what 
one observes when he passes through the country on a train; the 
objects which are near apparently go back at a high speed, while 
those which are far away seem to move very slowly. Now, in the 
case of the stars, if the rate at which they apparently go back were 
observed, their distances could be computed. If their motions in 
the backward direction were not enough so they could be observed 
in one year, then perhaps they could be observed in 10 years, or 100 
years. In this way the distances of all the stars which are not in 
the direction in which the sun is going, or in that from which it has 
come, could be determined. 

Unfortunately for the application of this method the stars are 
not at rest. The spectroscope and a study of their apparent motions 
show that on the whole they are moving at the rate of several hundred 
millions of miles per year. It follows that the distance of any one 
star can not be determined from its apparent backward drift because 
this depends not only upon the motion of the sun but also upon its 
own motion. But taking the stars as a whole their distances can be 
determined in this fashion. On the whole, they will not be moving 
in one direction more than another, and it is possible, therefore, by 
an averaging process for any group of stars, say of a definite mag- 
nitude, to find their average distance from the sun. 

The stars belong to two main types, depending upon the kind 
of light they send to us as determined by the spectroscope. The 
stars of Type I are those w r hich are blue, or bluish white, and are 
supposed to be in an early stage of their evolution. The stars of 
Type II are yellow T and similar to the sun. It is found that the stars 
of Type I of a given magnitude are on the average considerably 
farther from us than those of Type II. 

A statistical study shows that on the average first magni- 
tude stars of Type I are so far away that it takes their light about 
one hundred years to come to the earth, while light from first mag- 
nitude stars of Type II comes to us in about 43 years. The formulas 
on which the computations are made are based upon stars of the first 
nine or ten magnitudes. They are probably not very exact for the 
brighter stars, because there are too few of them to make the statis- 
tical method very safe; and they are probably inexact for the very 



ASTRONOMY 219 

faint stars, because they have not been used in deriving the formulas. 
But applying the formulas it is found that on the average the light 
of the ninth magnitude stars of Type I is more than 700 years com- 
ing to us, and of Type II a little more than 300 years. From the 
same formulas it is found that the light of stars of the fifteenth mag- 
nitude of Type I reaches us more than 3,000 years after it leaves the 
stars which radiated it, and of Type II, more than 1400 years. 

In getting these results it has been necessary not only to observe 
the apparent motions of the stars but to know the rate at which the 
sun is moving relatively to them. The motion of the sun is deter- 
mined by means of the spectroscope. The velocities of many stars 
relative to the sun are found, and by an averaging process it can be 
determined from these data in what direction the sun moves and 
with what speed. Thus we have the remarkable result that the 
spectroscope, which can not be used in measuring distances directly, 
is indirectly used in determining the distances of stars so remote 
that the ordinary means entirely fail. It is characteristic of science 
that various methods are woven together to secure its results. 

In order to determine the magnitude of the sun relatively to 
other stars we can compute how bright it would be if it were at the 
distance of the average first-magnitude stars of either Type I or 
Type II. The direct measurements of the light received from the 
sun show that its magnitude is about —26.4, and it follows that if 
it were at the average distance of the first-magnitude stars of Type 
I it would be only a little brighter than an eighth-magnitude star, 
or ni-Q as bright as an average star of Type I. If it were at the average 
distance of the first-magnitude stars of Type II it would be of the 
sixth magnitude, or about to"o as bright as the average star of Type 
II. It is thus apparent that our sun is considerably below the average 
of other suns in magnitude. 

Groups of Stars. The results given in the preceding section 
refer to stars as a whole and do not take into account their groupings. 
Just as the sky is seen to contain groups of stars, so the measure- 
ments of their positions with the telescope show that in many places 
in space large numbers are grouped in relatively small volumes. 
Among the best-known groups are the Pleiades, Fig. 41, the Hyades, 
Fig. 35, the Coma Berenices, Praecepe, Cancer, and Orion. While 
they differ greatly among themselves, a general idea of their enor- 



Fig. 100. Photograph of the Pleiades Showing the Nebulous Material Which Surrounds the Principal Slarb 



ASTRONOMY 221 

mous dimensions and splendid character can be obtained from a 
description of the Pleiades. The seven brightest stars of the Pleiades 
cover nearly three square degrees of the sky and, as was stated in 
the discussion of the constellation Taurus, they are so far away 
that it takes their light nearly 300 years to come to us. At this 
distance the sun would appear as an insignificant ninth-magnitude 
star. The Pleiades average more than one hundred times as great 
as the sun in light-giving power. The distances between the stars 
of this group are such that it requires several years for light to pass 
from one to the other. Besides the seven stars which are visible to 
the unaided eye, the telescope shows 45 others which have the same 
motion in both direction and speed and whose spectra are similar. 
They are undoubtedly a part of the same great family of stars. 
In addition to these stars there are about 2,000 fainter ones, which 
so far have not been examined with sufficient care to enable us to 
determine whether they arc really members of the same group or not. 

With the most powerful instruments and under good con- 
ditions some of the stars of the Pleiades are seen to be surrounded 
by very faint nebulous masses. When photographed with reflecting 
telescopes, which are peculiarly suited for bringing out the details 
of very faint and diffuse objects, the principal stars of the Pleiades 
are seen to be entirely surrounded by enormous masses of nebulous 
matter reaching almost from star to star. Fig. 100 is a photograph 
of this region taken at the Yerkes Observatory. The magnificence 
of a great group of stars averaging more than one hundred times the 
splendor of our sun, and of such dimensions that it takes light years 
to travel from one to another, and all enshrouded in huge masses of 
nebulous material is enough to stagger the imagination. Surety these 
stars in a very real sense form a family and have had a common origin. 

Long exposure photographs of the Pleiades' region covering 
the neighboring sky show that surrounding them there are Aery 
faint nebulosities which cover a region more than 10 degrees square. 
These nebulous masses are incomparably greater in extent than 
those which are shown in Pig. 100. 

In addition to the scattered groups of stars, such as the Pleiades, 
there are other groups which are in some respects more wonderful. 
They cover very small portions of the sky, generally much less than 
the apparent size of the moon, and contain in these small areas 



222 ASTRONOMY 

from 3,000 to 60,000 stars. There are more than 100 of these systems 
known, and they are found in all parts of the sky, especially in or 
near the Milky Way. Fig. 101 shows one of these magnificent star 
clusters which is situated in the constellation Hercules. The stars 
in these clusters are not only individually invisible without a tele- 
scope, but taken all together they can not be seen without optical aid. 




Fig. 101. The Great Star Cluster in Hercules 

They are generally very faint, ranging from the twelfth to the six- 
teenth magnitude. It is a question of the highest interest whether 
these systems are made up of great suns like our own, which appear 
feeble and near together only because of their enormous distances 
from us, or whether they are small suns closely crowded together 
and of not very great distance from us. If the latter hypothesis is 



ASTRONOMY 223 

correct they have had a peculiar evolution quite different from that 
of the great mass of stars. It has not been possible so far to measure 
directly the distance of any globular cluster. We can make only 
an inference of their remoteness in the sky from their relative fixity 
on the celestial sphere. Thus far observations have not shown any 
direct motions of any of the star clusters. In one or two cases observa- 
tions have shown the motions of an individual star in them, but it 
seems probable at present that these stars are only apparently in 
the clusters. It must be remembered that since stars cover rather 
thickly nearly the whole sky, there will be some ir the direction of 
the clusters, and apparently in them, which do not actually belong 
to them. If such a star were much nearer to us than the cluster a 
moderate motion would give it the appearance of moving rapidly in 
the cluster. 

To summarize, the facts are that no cluster as a whole has been 
observed to have any motion on the celestial sphere, and only a very 
few individuals of certain clusters have been found to have motions 
in the clusters themselves. We infer from their fixed positions on 
the sky that they are actually very remote from us. Of course, time 
will reveal their actual motions and permit us to make more than a 
conjecture. At the present time it seems very probable that they 
are distant at least 400 light years. At any rate, we may make the 
assumption in order to obtain some sort of a mental picture of what 
a cluster really is. At that distance our sun would appear as an 
eleventh-magnitude star. If the assumption is correct, it follows 
that the stars of the clusters are somewhat fainter than our sun 
though comparable to it. The more interesting question is how 
far they are from one another. A computation shows that in the 
star cluster whose photograph is given in Fig. 101, where in its center 
the stars seem to touch one another and where there seems to be 
imminent danger of collision, the distance of one star from another 
is on the average 30,000 times as far as the distance from the sun 
to the earth; or, in round numbers, the distance from one star to 
another in Fig. 101 is 30,000 times 100,000,000 miles. Since gravita- 
tion varies inversely as the square of the distance, it is not surpris- 
ing that the interactions of these stars on one another do not pro- 
duce sufficient motions to be observed in the short time they have 
been followed by our great telescopes. In these clusters there is 



224 ASTRONOMY 

abundant room for almost permanent motion of the stars without 
any danger of collisions, and each sun might be accompanied by a 
retinue of planets without their being in any particular danger of 
destruction from other suns. 

A remarkable peculiarity of the stars of some of the clusters 
is that a considerable fraction of them vary in the light they radiate. 
The period of variation is almost the same for the variable stars of 
one cluster but may be somewhat different for those of another. 
The periods are generally about a day. The light from the stars is 
sensibly uniform except for a short time when it flashes out with 
from two to six times its ordinary brilliance. More than 500 of this 
type of variables have so far been found. There is no explanation 
for this most peculiar variability. 

Recent measurements of the distances and motions of the stars 
show that our own sun is a member of a rather open cluster of per- 
haps about 100 stars. Our great distance from all other suns gives 
us an idea of the distances separating the stars in the clusters. 

Double Stars. A few double stars have been known since 
the invention of the telescope. They are tw T o suns which are so near 
together that they appear as a single one without an instrument. 
In modern times the limits are still closer than this definition would 
lead one to infer, for a star is not considered as being a real double 
unless the distance separating its components is less than 0.1 of that 
which is the limit of visibility without telescopic aid. There are 
very many of these objects known at the present time, and in Burn- 
ham's great catalogue of double stars the observations and descrip- 
tions of about 13,000 are given. 

Originally it was supposed that our sun and planetary system 
is a type of all the systems in space, and consequently that double 
stars are simply examples of two suns happening to be in the same 
direction in space. A computation shows easily that the probabili- 
ties are against very many pairs existing in which two are seen almost 
exactly in the same direction and are not actually associated. About 
120 years ago Sir William Herschel began systematic observations 
of the double stars in order to determine their distances; for it was 
clear that if they were only apparently in the same direction, and one 
many times as far away as the other, the near one would apparently 
move with respect to the remote one while the earth was making its 



ASTRONOMY 



225 



revolution around the sun. Herschel did not find what he was look- 
ing for, but was surprised to observe after a few years that in some 
cases the two stars were going around their common center of gravity. 
This established the existence of systems of two suns revolving near 
each other, and furnished a model quite different from that of a 
single sun attended by a family of planets. 

The discoveries which Herschel's successors have made with 
modern telescopes have shown that these double-star systems are 
very numerous, and the number known is constantly being added 
to by the observations which are carried on at all the leading obser- 
vatories. Those stars which form an actual physical system are 




Fig. 102. The Full Curve is the Apparent Orbit of the Companion 
of Sirius; the Dotted Curve Its Actual Orbit 



called binaries. The periods of the binaries range from about five 
years to hundreds, and perhaps thousands, of years. The orbits of 
those whose periods are very long are, of course, not well known 
because of the short time covered by the observations. The stars 
whose periods are short are near one another, and the stars whose 
periods are long are on the whole very remote from one another. Fig. 
102 shows in a dotted curve the real orbit of the companion of Sirius 
with, respect to the principal star, which is represented by a small 
circle where the axes cross. The plane of the orbit is tipped through 
an angle of about 45° around the line L. Consequently, instead 
of seeing the companion move along the dotted ellipse, we find it 
moving along the full line ellipse, which is the projection of the other. 



226 



ASTRONOMY 



TABLE VIII 
Binary Stars Whose Masses and Distances Are Known 



Star 


Semi-axis 


Period 


Mass 


Light 


Eccentricity 


Alpha Centauri 


23.6 


81 


2.0 


1.7 


0.53 


Sirius 


21.7 


52 


3.7 


32.0 


0.62 


Procyon 


10.0 


40 


0.6 


8.5 




Eta Cassiopeiae 


41.0 


196 


1.8 


1.0 


0.51 


70 Ophiuchi 


24.0 


88 


1.8 


0.7 


0.50 


85 Pegasi 


19.5 


24 


11.3 


2.2 


0.59 

1 



The apparent distances of double stars from each other are 
determined by direct observations with the telescope. Their actual 
distances from each other can not be found unless their distances 
from the earth are known. In a few cases the distances of binary 
stars are known, and in these cases the real distances of the two 
members from each other can be determined. When the distances 
of two stars from each other and their periods of revolution are known, 
their masses can be found just as the mass of the planet can be found 
from the period of a satellite which revolves around it at a known 
distance and in a known period. Also, when the distances of the 

stars are known, their lum- 
inosity compared to that of 
the sun can be determined. 

There is one striking differ- 
ence between the orbits of 
binary stars and the orbits 
of the planets in their mo- 
tions around the sun. While 
the planetary orbits are 
nearly round, the orbits of the 
binary stars are, on the whole, very elongated. The average eccen- 
tricity of those which are best known is in the neighborhood of 0.5. 
Table VIII gives the stars whose distances, actual orbits, masses, 
and light in terms of the sun's light are known. In column one is 
the name of the star ; in column two, the semi-axis of its orbit expressed 
in terms of the mean distance from the earth to the sun; in column 
three, the period expressed in years; in column four, the mass 
expressed in terms of the sun's mass; in column five, the light 




Fig. 103. The Shift in the Spectral Lines of a 
Binary Star 



ASTRONOMY 227 

expressed in terms of the light radiated by the sun; and in column 
six, the eccentricity of the orbit. 

Spectroscopic Binary Stars. In many cases there are two stars 
which are so remote and so close together that they appear as one 
when seen through the most powerful telescopes. The spectroscope 
has enabled us under certain circumstances to determine, neverthe- 
less, their binary character. If a star is coming toward us, the lines 
in its spectrum are shifted toward the violet end, just as when a 
locomotive is approaching us the pitch of its whistle is raised. The 
approach of a star crowds the waves closer together and changes 
the color toward the blue end of the spectrum. Our eyes are not 
sufficiently sensitive to slight differences in color to enable us to 
detect this change, but it is possible in many cases to measure the 
shift in the spectral lines. A star receding has its lines shifted corre- 
spondingly toward the red end of the spectrum. 

Suppose the circle in Fig. 103 represents the orbits of two equal 
stars revolving around their center of gravity in the direction 
indicated by the arrow on the orbit. Suppose the earth is extremely 
far away in the direction indicated, and that the two stars appear 
single as seen through even the most powerful telescopes. Suppose 
also that they are chemically and physically the same, so that they 
have like spectra. Consider the system when one star is at A x and 
the other at B ± . In this position the star at A ± is receding from the 
earth and the star at B 1 is approaching toward it at an equal rate. 
Therefore, the spectrum of the star A l will be shifted toward the 
red, and the spectrum of the star B x correspondingly toward the 
violet. The spectrum then will be composed of double lines whose 
distance apart will depend upon the relative velocities of the stars. 
For the velocities which are actually found the lines are always very 
close together. 

Now, consider the system again when A x has moved forward 
to A 2 and B 1 to B 2 . In this position the stars are neither approach- 
ing nor receding and their lines all appear single. When A 1 and B x 
have changed places the lines again appear double. The period of 
revolution is the time between the one doubling of the lines to the 
second following doubling. 

In this way the existence of binary stars is not only proved, but 
it is possible to find out more about the orbits than is generally the 



228 ASTRONOMY 

case in ordinary visual binaries. The spectroscope shows not only 
the periods, but the velocities, of the stars in their orbits, from which 
we can compute their actual dimensions. Knowing the dimensions 
of the orbits and the periods, the masses can be found. The spec- 
troscopic observations do not enable us to determine the distances 
of the stars from us and, therefore, we cannot determine their 
brightness. 

Besides the spectroscopic binaries of the type just described, 
there are many others in which one of the two stars is so faint that 
its spectrum can not be observed. In such cases the star whose 
spectrum is visible shifts alternately toward the violet and the red 
ends of the spectrum. The period of the shift shows the period of 
revolution of the pair, and the amount of shift shows the dimensions 
of the orbit of the brighter star. It is not possible in this case to 
determine the exact masses because this determination depends 
upon the distance of the stars from each other, and this can not be 
determined from the distance of one alone from its center of gravity. 
A sort of lower limit to the masses can be found because the distances 
of the stars from each other must be greater than that of the more 
luminous one from its center of gravity, and in general will be more 
than twice that great. 

There is another uncertain factor in the determination of these 
orbits, viz, the angle which the plane of the orbits makes with a line 
joining the stars with the earth. In the diagram and in the discus^ 
sion so far it has been assumed that the plane of their orbit passes 
through the earth. It is obvious that in general it will be inclined 
to the line from the stars to the earth. Consequently, instead of 
having the total velocity of the stars in the case of the double lines, 
we shall have only that component which is toward the earth. This 
leads us in general to a too small value for the combined masses of 
the system. 

The study of binary stars by means of the spectroscope was 
begun in 1889 and most of the work in it has been done since 1900. 
In 1905 there were 136 spectroscopic binaries known, and on January 
21, 1910, there were 306. The number of orbits of those which are 
fairly well determined is now about 70. The periods range from less 
than five hours up to nearly two years. The distances apart of the 
components vary from 50,000 miles as a lower limit to nearly 



ASTRONOMY 229 

105,000,000 miles. The eccentricities vary from practically zero to 
about 0.9. On the whole the stars with the shorter periods have 
the smaller eccentricities. 

Variable Stars. The variability in the light of certain stars in 
the globular clusters was mentioned above. There are many other 
stars whose light varies in different ways. The first one known was 
Omicron Ceti, discovered in 1596. The next one was Algol (the 
Demon), discovered in 1783. Variable stars were not known in any 
considerable numbers until near the close of the nineteenth century, 
and now more than three hundred of these objects are in the cata- 
logues. 

In one type of variables the light of a star remains constant 
except for short intervals when it diminishes greatly in brightness. The 
typical star of this type is Algol, and there are about twenty-five such 
stars known. Their periods are generally less than five days. The 
explanation of their variability is that they consist of two stars, one 
of which is relatively dark, revolving around their center of gravity 
in a plane passing through the earth. The bright star shines with its 
customary brightness except when the dark star passes between 
the luminous one and the earth, and then its light greatly diminishes. 
It is obvious that these systems are in most respects analogous to 
the spectroscopic binaries and, indeed, in most if not in all cases the 
lines of the brighter component shift in a way which proves their 
binary character. The star Algol has a period of two days, 28 hours, 
48 minutes, and 55 seconds. It is normally a star of the second mag- 
nitude, but at the time of eclipse it loses five-sixths of its light. This 
is a spectroscopic binary and the orbit of the brighter component is 
consequently known. Its distance from the center of gravity of the 
system is about 1,000,000 miles. From the duration of the eclipse 
and the rate at which the light fades and returns, it is possible to 
compute the diameters of the bright and faint stars. In the case of 
this star the bright component has a diameter of approximately 
1,000,000 miles and the dark component 800,000 miles. From meas- 
urements of the distance of this pair, which unfortunately are sub- 
ject to some error, it is found that the bright component radiates 
80 times as much light as our sun. Taking into account the area 
of its surface, it follows that it radiates 52 times as much light per 
unit area as the sun does. 



230 ASTRONOMY 

There are several slight variations from the type exemplified 
by Algol. One is that in which the stars are of unequal size but 
both bright. Then each eclipses the other in turn during their 
revolution. The star Beta Lyrae is an example of another type 
closely related to the Algol variables. The chief differences are 
that the light varies continuously from its maximum to its mini- 
mum and back to its maximum again. There are generally two 
minima and a single maximum. The explanation of these stars is 
that the two components revolve very near together and in a plane 
passing through the earth. Under these circumstances as soon as 
the first star passes out of its eclipse by the second, it immediately 
begins to eclipse the second. One minimum is when the fainter is 
between the earth and the brighter, and the other minimum is when 
the brighter is between the earth and the fainter. Of course, if the 
two were equal in all respects there would be a single minimum. 
The maximum is when the line joining the stars is at right angles 
to the line joining them with the earth, at which time the earth 
receives the full light of both of them. These stars have been found 
from the variation of light and the shifts of their spectral lines to 
be of enormous dimensions and very tenuous. 

There is another type of variable stars of which Omicron Ceti 
is the best-known example. This star has been observed through 
more than 300 of its cycles. The periods of these stars are long and 
irregular. The time for minimum to maximum is generally con- 
siderably shorter than from maximum to minimum. The maxima 
and minima are subject to great irregularities, and there is no dis- 
coverable relation of them to the period. According to the observa- 
tions of Sir William Herschel the star Omicron Ceti changed its light 
more than 10,000 fold in only four years. The spectroscope showed 
marked changes in the spectra of these stars, but no evidence of 
their being spectroscopic binaries. They are generally red stars 
which seem far advanced in their cooling, but we can imagine no inter- 
nal disturbances which would cause the enormous fluctuations in 
their radiating power that is often observed. 

There are besides the stars of the Omicron Ceti type others 
whose variations give no hint of periodicity. Some are characterized 
by their light suddenly flashing out with great brilliance, usually 
after intervals of many years of quiescence, and others unaccount- 



ASTRONOMY 231 

ably fade away and become invisible even through the most power- 
ful telescopes. These stars are also generally red and sometimes 
apparently associated with faint nebulous masses. 

Temporary Stars. Occasionally stars have been observed to 
blaze forth suddenly in parts of the sky (so far always in the Milky 
Way) where none had previously been seen, and then to sink away 
quickly into obscurity. They are characterized by a very sudden 
rise to a great maximum which in spite of later possible increases 
is never repeated. One of the most remarkable of these was observed 
in Cassiopeia in 1572, and was mentioned in the discussion of this 
constellation. 

One of the recent remarkable stars of this type appeared in 1901 
in the constellation Perseus. On February 19 of that year a photo- 
graph of the region where it later appeared was taken and did not 
show it. By the 23d it was brighter than the star Capella. In this 
short interval its light had increased more than 20,000 fold. A day 
later it had lost one-third of its light, and it steadily decreased in 
brightness until about the 22d of March, when it flashed up. It 
then diminished again until the 24th of April, when it had gone down 
to the sixth magnitude. At this time it flashed up again nearly to 
the third magnitude, after which it faded away and became entirely 
invisible by the end of the year. 

The explanation of these temporary stars is that they are dark 
suns moving swiftly through space and that they suddenly encounter 
invisible dust clouds or nebulous material. Striking these tenuous 
masses with high speed, their surfaces are suddenly made to glow 
with a brilliant light analogous to that of the tiny meteors when 
they dash into our atmosphere. Since the surface only is heated 
the light speedily fails when the star passes through the material 
with which it collides. Secondary collisions with dark masses of the 
dust clouds or nebulous material cause the secondary flashes that 
sometimes are observed in these stars. The star Nova Persei was 
photographed a few months after it blazed forth and was found to 
be surrounded by a very faint nebulous mass. The explanation is 
that the nebulous matter which had previously been dark and 
invisible, became visible as it was lighted up by the glowing star. 
The star Nova Persei was so far from us that it took its light approxi- 
mately 300 years to reach us. This means that the collision, instead 






Fia 104 P, 



— 



NVhulou> M rial in Cygnu Photographed al the Xerkes ObservatoH 



ASTRONOMY 233 

of taking place in 1901 when the star was observed, actually took 
place about the year 1600. 

Nebulas. Scattered here and there throughout space are great 
cloud masses of low luminosity known as nebulas. They are 
supposed to be the primitive world stuff out of which suns are 
made in very early stages of their development. Fig. 104 is a photo- 




Fig. 105. The Trifid Nebula 

graph of an extremely widespread, gaUze-like, nebulous mass which 
is so faint that it is visible only in a very large telescope. This is 
about the most primitive type of world stuff with which we are 
acquainted. It suggests that the process of creation, or of evolution 
of matter from something more primitive, was not an event which 
took place at any one time and then stopped, but rather one which 



234 ASTRONOMY 

always has been and always will be taking place. That is, these 
photographs suggest that creation is a process continuously going 
on rather than one confined to any particular time. If this idea is 
correct the nebula whose photograph is shown in Fig. 104, is matter 
recently created, using recently in the astronomical sense. 




Fig. 106. A Spiral Nebula in Ursa Major 

There are other nebulas which show a considerably higher 
degree of organization of matter as, for example, that in Orion, 
Fig. 43. There are others still farther advanced, as shown in Fig. 
105. In addition to these more or less irregular nebulous masses, 
there are the spirals which exhibit a high degree of organization and 
to which we shall have occasion to refer in discussing the origin and 
evolution of the solar system. Fig. 106 shows one of these spiral 



ASTRONOMY 235 

nebulas which is in the constellation Ursa Major. There are still 
others associated with stars; and some, called "planetary nebulas/' 
have the general appearance of a planet. 

All the nebulas except the spirals have bright-line spectra 
instead of dark-line spectra like those of the sun and stars. This 
shows, in accordance with the principles of spectrum analysis, that 
the nebulas are masses of incandescent gas rather than luminous 
solids or liquids shining through cooler gases. Before these results 
were obtained by the spectroscope it was supposed that perhaps 
the nebulas were other galaxies of stars so far away that their individ- 
ual members were not separately visible. The spectroscope, how- 
ever, proves they are gaseous and this conclusion is in harmony 
with other considerations regarding the evolution of suns. 

COSMOGONY, OR THE EVOLUTION OF WORLDS 

Evolution. A slow change in one direction, especially if it 
be from the simple and unorganized to the complex and organized, 
is said to be an evolution. The central idea of it is that the change 
from one state to another is an orderly and continuous one rather 
than a chaotic and abrupt one. When considered in this way it is 
seen that evolution is simply a statement that the organization of 
the universe which makes science possible is extensive in time as 
well as in space. 

In order to discover the evolution of any part of the physical 
universe it is necessary to know the condition of it at a given instant 
and the laws according to which it changes. For example, in order 
to determine the evolution of the solar system we must know its 
condition at one time and how its various members change. In the 
preceding pages a description of the solar system has been given 
and a synopsis of the chief laws which it obeys. If all of the data 
and all of the laws of change were known, and if one possessed 
sufficiently powerful mathematical processes for making the solu- 
tion, then it would be possible to predict the condition of the solar 
system for indefinite time in the future, and to find what it had 
been for indefinite time in the past. Unfortunately, we are never 
able to determine fully all the factors which are involved in a series 
of changes, and it is equally certain that we do not know with 
absolute exactness all of the laws to which the system is subject. 



236 ASTRONOMY 

For example, the temperature of a given place on the earth 
depends upon the temperature and the distance of the sun, the way 
the distance from the earth to the sun changes, the period of the 
earth's rotation, and many other factors. A great many of the 
determining factors are known exactly, or at least with a high degree 
of precision, but some are totally unknown. If the most important 
of them are known with a considerable degree of accuracy, predic- 
tions can be made with corresponding accuracy even though some 
of them remain unknown. Thus, in the case of the temperature of 
the place just mentioned, while many factors are unknown, predic- 
tions which are on the whole reliable can be made on the basis of 
those which are known. For ages to come the succession of seasons 
and of day and night at any one place can be accurately described. 
But it is not possible to predict the precise temperature changes even 
for a short time. Thus, we see that while it is possible to work out 
a general idea of the nature of the temperature changes, it is not 
possible, because of the imperfections of our knowledge, to describe 
them with absolute precision. The degree of accuracy decreases 
as a rule with the extent of time over which our predictions extend. 
The chief reason is that there may be certain factors at work which 
are unknown and relatively insignificant for a short time, but which 
in the long run become very important. Thus, in the case of the 
climate at a particular point of the earth, we can predict the changes 
of seasons and of day and night and the mean temperatures with a 
considerable degree of accuracy for a short and also for a very long 
time if we know all the factors involved. But if there is some unknown 
cause which will continually lower the temperature of the sun at a 
very slow rate, then our predictions will be almost true only until 
sufficient time has elapsed for this unknown cause, operating in one 
direction, to produce important results. 

A theory of evolution is extremely valuable in many ways and 
at the present time is considered as having a legitimate place in the 
discussion of every science. In the first place, it shows us what 
facts are important and what are not, because, in attempting to 
develop a theory of the changes through which a system goes, we 
must relate all the facts to one another. If there are any contra- 
dictions among them, and among minor theories based upon them, 
they will be revealed in our attempts to weave all of them together 



ASTRONOMY 237 

into one systematic, harmonious whole. For example, if our con- 
clusion, based on more or less uncertain observations, that Mercury 
has one face always toward the sun contradicts something funda- 
mental in the system, we should be likely to find it out in the con- 
sideration of its evolution. Therefore, if we are considering only 
the facts and minor conclusions regarding any domain of science, 
we see that the attempt to construct for it a theory of evolution is 
of the highest importance because it compels a more careful examina- 
tion of these things which we are supposing are important. 

In a somewhat similar manner the consideration of a question 
in a large way often directs our attention to gaps in our knowledge 
which ought to be filled. In the biological sciences the theory of evolu- 
tion has directed inquiry in thousands of directions to supply addi- 
tional data. While this has not been true in astronomy to the same 
extent, yet the theory of evolution has there raised many new ques- 
tions and stimulated important investigations. 

A theory of evolution is also valuable in that by discovering 
what the conditions will be in the future it makes it possible for us 
to adjust ourselves to them, or in some cases to control events for 
our good. An example of this, a matter of such universal experience 
that it has become commonplace, is that in the summertime we pre- 
pare for the winter because we know that it is sure to come. In a 
larger way, particularly in the biological sciences, it may be possible 
to foresee things in the remote future for which we as a race should 
prepare ourselves. 

Finally, a theory of evolution is of importance for the satis- 
faction it gives in contemplating the subject as one grand whole. 
It is related to separate facts and minor theories upon which it is 
based as a beautiful and finished house is to unsightly heaps of stone, 
brick, and wood from which it might be built. Laplace commenting 
on the satisfaction obtained in considering astronomy as a unit, 
said: "Contemplated as one grand whole it is the most beautiful 
monument of the human mind, and the noblest record of its intel- 
ligence." 

Historical. The theory of the evolution of the solar system, 
and, indeed, of all the stars that fill the sky, was first begun in what 
would now be considered an approximately scientific manner by 
Thomas Wright of Durham, England, who published a volume on 



238 ASTRONOMY 

this subject in 1750. He supposed that the Milky Way was com- 
posed of a vast number of solar systems similar to our own, spread 
out in a great double ring which rotated around an axis perpendicular 
to its plane. He treated the solar system as an example illustrating 
the dynamics of the sidereal system. His work was not adequately 
based on observations and contained many serious errors. This, 
of course, was only to be expected in pioneer work in so difficult a 
subject. 

The work of Wright fell into the hands of the brilliant phi- 
losopher Kant, who was then a young man. His vivid imagination 
quickly ran beyond the bounds of what Wright had set forth. He 
saw some of the weaknesses of Wright's theory and the possibility 
of adding greatly to it. In 1755, he published a book on the subject 
agreeing in many respects with that of Wright, but which, on the 
whole, was vastly superior to it. He supposed that in the beginning 
all the material which now makes up the sun and planets and other 
members of the solar system was in a widely-scattered primitive 
condition of un-united elements. He supposed that the chemical 
affinity of one element for another caused compounds to be formed, 
thus setting up motions. As atom united with atom to make com- 
pounds, so molecule united with molecule under gravitative forces 
and made continually larger and larger masses. As masses of con- 
siderable dimensions were formed so that they became strong centers 
of attraction, considerable motions were developed. In some obscure 
way he supposed the motions in all directions, except that in which 
the planets moved, were destroyed by collisions, leaving a number 
of planets revolving in a definite plane. Kant considered in succes- 
sive chapters of his book the densities and rotations of the planets, 
the eccentricities of the orbits, the origin of comets, the origin of 
satellites, the origin of the rings of Saturn, the zodiacal light, and 
the theory of the constitution and condition of the sun. 

The beauty and generality of Kant's theory, as well as the 
attractive manner in which he set it forth, are very enticing, but 
when considered calmly in the light of modern knowledge, particu- 
larly in the light of dynamics, it is found to have some serious and 
fatal faults. Notwithstanding this, there are many very valuable 
contributions in it to the subject, and it is a stimulating book to read 
even at the present time. 



ASTRONOMY 



239 



The world was not prepared for the ideas of evolution in 1755, 
and the work of Kant attracted only very little attention. But in 
1796 a great French astronomer, named Laplace, at the end of a 
charming popular book on astronomy, explained in a few pages 
his ideas of how the solar system may have arrived at its present 
condition. This was written apparently without any knowledge 
on the part of Laplace of the work of either Wright or Kant. Laplace 
introduced the discussion by calling attention to the remarkable 
regularities in the solar system. He commented on the fact that the 
planets all revolved around the sun in the same direction nearly in 
the same plane. He calculated that this condition would be the 
result of chance only once in some 500,000,000 cases, showing, there- 
fore, that in all probability it was due to some initial state from which 
it had systematically developed. He likewise called attention to 
the remarkable circularity of the orbits and the directions of rotation 
of the planets, etc. 

In outline the theory of Laplace is that originally the solar atmos- 
phere was a nebulous envelope in an intensely heated condition, 
and that it extended out beyond the orbit of the farthest planet. 
He supposed the whole mass rotated as a solid in the direction in 
which the planets now revolve. It was supposed in this theory that 
the dimensions of the system were maintained by gaseous expansion 
the same as the dimensions of the sun or the earth's atmosphere are 
at present. This great nebulous mass would lose heat by radiation 
into space and consequently would contract. 
If such a rotating mass contracted, it would 
continually rotate faster and faster for the 
reasons set forth in discussion of the question 
of the uniformity of the earth's rotation. If 
a mass rotates faster, the tendency for the 
material at its equator to fly off because of the 
centrifugal acceleration continually increases. 
Laplace said that it seemed reasonable that 
the contracting solar mass would reach such 
a state that this tendency of the particles at 

its equator to fly out would exactly balance their tendency to go in 
because of the attraction of the mass interior to it. When this state was 
reached he supposed a ring would be left off, as is indicated in Fig. 107. 




Fig. 107. The Laplacian 
Ring Theory of the 
Origin of the 
Planets 



240 ASTRONOMY 

Unless the ring were perfectly circular and uniform, and sub- 
ject to no disturbing influences, it would have a tendency to break, 
Laplace thought, at some place and to concentrate on the place in 
it where there was the greatest mass. That is, if there were a nucleus 
on it at any point, this excess of matter would gradually draw to it 
all the rest of the whole ring, while it would continue to revolve 
around the sun in the same period as the ring did at the time it was 
abandoned. It seemed to him probable that the sun would go on 
shrinking after a ring was abandoned and that it would later leave 
off another, and then still another similarly, until it either arrived 
at a state of permanent equilibrium or had a density so great that 
it could no longer contract. 

Laplace then supposed the system of planets grew up from 
a system of rings abandoned successively by the sun, beginning 
with the outermost and ending with the innermost. The rings con- 
centrating would give rise to large, globular masses revolving around 
the sun at their respective distances from it. These globular masses 
might in turn be rotating so rapidly that they would abandon rings 
which in a similar manner would give rise to satellites. He sup- 
posed that perhaps Saturn's rings were examples of this process in 
which the satellites were not yet formed. 

This theory of Laplace pictures the earth as being at one time 
in a gaseous state. It was supposed that by losing heat it cooled 
off until a crust formed over its surface, leaving the liquid interior; 
and it was thought that the volcanoes were openings through the 
shallow crust into that liquid interior. This theory was widely 
accepted : first, because of the great name of its author; and second, 
because of its simplicity and harmony with the main facts of the 
system. It gave the geologists reasons for believing that the earth 
is very old, and encouraged them to draw conclusions respecting 
its age and evolution on the basis of geological facts. The half 
century following Laplace's work was characterized by most remark- 
able activities in geological science. The great age of the earth was 
fully established, and the innumerable fossils which filled the old 
rocks were brought to light in vast numbers. The work of the 
geologists paved the way for the zoologists. In 1858, Darwin extended 
the general ideas of evolution, which had their origin in astronomy 
and which had spread to geology, to the biological sciences by his 



ASTRONOMY 241 

publication of the "Origin of Species." It is questionable whether 
any other work of modern times has had so profound an influence on 
the thought of the world as this book by Darwin. Since its publica- 
tion the doctrine of evolution, aside from the details of its precise 
mode, has been almost universally adopted. Not only is science 
considered from the point of view of a changing universe, but history 
is interpreted in the light of it and its applications are extended to 
the political and social sciences, and even to religion. 

Test of the Laplacian Theory. There are two general ways 
of testing the truth of a theory. One is the determination of whether 
it is consistent with itself, and the other is whether it is in harmony 
with the facts given by observations. The former is generally the 
more difficult of the two, and in questions of physical science is 
largely of a mathematical nature. 

As Laplace himself pointed out, his hypothesis as to the ring 
origin of the planets is in agreement with the chief facts of the solar 
system. If the solar system originated in this fashion we should 
expect all the planets to be revolving in the same plane, or at least 
nearly in the same plane, and such is the case. If there were any 
deviations from strict agreement of the planes of revolution due to 
any irregularities in the original solar nebula, we should expect to 
find the greatest ones in the planets far from the sun, because as the 
sun continued to rotate there would be a tendency for it to become 
more and more uniform. Here the consequences of the theory are 
not so well in harmony w T ith the facts, for the orbits of the remote 
planets are on the whole much more nearly circular than those which 
are closer to the sun. Mercury has a more eccentric orbit than any 
other planet. According to this theory the planets should all revolve 
around the sun in the same direction, and this is found to be true 
in the solar system. According to the Laplacian theory the orbits 
should be very nearly if not exactly circular, and this is also almost 
verified in the solar system. If there were any deviations from sensible 
circularity it would be expected, according to the theory, that they 
would be the greatest in the case of the orbits of those planets which 
were far from the sun. Here the theory is not in so perfect harmony 
with the facts, because it is found that the orbits of the remote 
planets' are on the average more nearly circular than those closer to 
the sun, and that Mercury's orbit is the most elongated of all. 



242 ASTRONOMY 

While the Laplacian theory is in general harmony with the main 
facts furnished by observation, there are, nevertheless, some respects 
in which it is not entirely satisfactory. The question arises whether 
they are not sufficient to compel us radically to modify it. It is 
understood that it is easier to disprove a theory which is wrong than 
it is to establish one which is correct, for one example contradictory 
to an erroneous theory disproves it, while many examples of harmony 
with a correct theory only show that it is probable. A slight dis- 
agreement between the ring theory and the planes of the orbits of 
the planets and their eccentricities have been noted. There is much 
more serious disagreement when we come to a consideration of the 
orbits of the planetoids, which were not known when Laplace first 
formulated his theory. There are now about 700 known planetoids 
whose orbits vary from coincidence with the plane of the planetary 
orbits, to an inclination of nearly 40 degrees to it, and from sensibly 
perfect circularity to elongations nearly as great as those of some of 
the cometary orbits. These 700 orbits weave in and out among one 
another in such a fashion that if they were made of wire one could 
not be removed without taking all of them. According to the ring 
theory it is necessary to suppose that a ring was abandoned for each 
one of them. It is perfectly obvious that so complex a ring system 
intersecting itself, is entirely outside of the possibilities. For example, 
the orbit of Eros reaches out beyond that of Mars and down almost 
to that of the earth, and is highly inclined to the orbits of both planets. 
The ring theory asks us to suppose that a ring was abandoned, which 
later went into the planet Mars, then another highly inclined to the 
former and reaching beyond it, which went into the planetoid Eros, 
and then another from which the earth developed. The impossi- 
bility is apparent. 

Objections of quite another type are presented in the case of 
the satellites of Saturn and Jupiter. Each of these planets has a 
single satellite revolving around it in the retrograde direction. 
According to the Laplacian theory of the origin of the satellites, 
rings were abandoned at their respective distances and the planetary 
nebula contracting later abandoned more rings. It follows from 
this theory that all the satellites must necessarily revolve around 
their respective planets in the same direction. The fact that this 
is not so in two cases is a direct contradiction of the theory. 



ASTRONOMY 243 

It has been stated that as a body contracts it rotates faster 
and faster. Consequently, since by the Laplacian hypothesis the 
planets have contracted from the dimensions of their satellite orbits, 
every planet must rotate in a shorter period than that of the revolu- 
tion of its innermost satellite. This certain consequence of the theory 
is violated in the case of the inner satellite of Mars, which makes 
its revolution in about eight hours while Mars turns on its axis in a 
period of some 24 hours. There is also an important discrepancy 
between theory and observations in the case of the inner ring of 
Saturn, the particles of which make a revolution in about five hours 
while the planet rotates on its axis in a period of a little more than 
10 hours. 

According to the Laplacian theory, the more remote planets are 
older than the interior ones. The excess of their ages is not known, 
but certainly it must be very great according to the theory. Perhaps 
Saturn is a thousand times as old as the earth. When we consider 
how much greater its orbit is than that of the earth, and how long 
it must have taken the sun to contract from the dimensions of the 
earth to its present size, this does not seem an unreasonable estimate. 
It follows that if Saturn were originally in a state similar to that 
of the original earth it should be much farther advanced in its evo- 
lution. It was seen in the discussion of planets that Saturn is yet 
in a very primitive state. Of course, being larger, it would undergo 
its evolution more slowly, but it seems to strain the probabilities of 
the matter to suppose that its difference in size could offset its 
supposed great difference in age. It is thus seen that the Laplacian 
theory is in many places in direct conflict with the observations. 
These discrepancies, however, have nearly all been discovered since 
the theory was originally formulated. 

About ten years ago Professor Chamberlin and the writer 
undertook to make a critical examination of the Laplacian theory, 
both for internal discords and harmonies, and to find disagreements 
and agreements with the facts given by observation. This study 
revealed inconsistencies in the theory itself, as well as contradictions 
to the observed phenomena, some of which have been noted above, 
which compel its radical modification. It is certain now that the 
ring hypothesis as to the origin of the planets can no longer be held 
as a possibility. This does not mean that the Laplacian theory has 



244 ASTRONOMY 

not been of the greatest importance in the development of science, 
but it simply indicates that greater knowledge has shown us its 
imperfections, and how we may use it as a stepping-stone to a more 
perfect picture of the origin and evolution of the solar system. 

Planetesimal Theory. The solar system exists and is in the 
midst of an evolution; the problem is to trace out the mode of this 
evolution. The Laplacian theory has been seen to have fatal weak- 
nesses and to be no longer tenable. We shall now outline a theory 
which has been developed by Professor Chamberlin and the author 
to take its place. 

Instead of supposing that the solar system started from a vast 
gaseous mass in equilibrium under the law of gravitation and the 
laws of gaseous expansion, the Planetesimal Hypothesis postulates 
that the matter of which the sun and planets are composed was at 
a previous stage of its evolution in the form of a great spiral swarm 
of separate particles whose positions and motions were dependent 
upon their mutual gravitation and their velocities. Gaseous expan- 
sion preserved the dimensions of the Laplacian nebula but had no 
sensible influence in the spiral. Because of the fact that every 
particle according to this theory is considered as being an essentially 
independent unit it is called the planetesimal theory. Before consid- 
ering in detail the planetesimal hypothesis, and before proceeding to 
a discussion of its merits, attention should be called to the fact that 
there is not in all the heavens a single example known of a nebula 
of the Laplacian type. On the other hand, recent discoveries, par- 
ticularly those made at the Lick Observatory, show that the spiral 
nebula is not only a common form but is, indeed, the dominant 
type.- There are within range of our instruments at least ten times 
as many of them as of all other types combined, and they range in 
extent and brightness from the great Andromeda nebula down to 
small faint masses which are barely distinguishable with long expo- 
sure photographs taken with the most powerful instruments. 

Before considering the evolution of our system from a spiral 
nebula, a suggestion as to its origin will be developed. It is, of course, 
understood that the theory is independent of the correctness of this 
suggestion. It has the merit of giving us a full picture of the course 
of evolution and of showing the dynamical condition of a nebula. 
It has been seen above that there are within the range of our present 



ASTRONOMY 



245 



instruments at least a hundred millions of suns, and it is found, from 
the observations of their apparent motions and their actual motions 
in the line of sight by means of the spectroscope, that on the average 
they are moving with high speed. Though there are undoubtedly 
parallelisms and some degree of orderliness in their motions, never- 
theless, it is almost certain that now and then two suns will pass 
near each other. A computation, based on suppositions which seem 
to be reasonable as to the dimensions of the sidereal system and the 
number of stars in it, shows that in the long run a given sun will 




Fig. 108. The Origin of Elliptical Orbits of Matter Ejected 
from the Sun at the Time a Star is Passing 

pass near enough to another sun to cause serious disturbances about 
once in a billion years. 

Now consider a star passing near our sun, and remember that 
the latter is a highly heated body subject to explosive forces which 
even at frequent intervals hurl matter up from its surface to heights 
of several hundred thousand miles. In Fig. 108 let S represent our 
sun, and the orbit of a star passing by it. Consider the visiting 
star when it is at the position S x . It raises enormous tides on our 
sun, their height depending upon its distance and mass. One tide 
is on the side toward S 1} and the other tide on the opposite side. 
Instead of being a few feet high, it is reasonable to suppose that 
they are many thousands of miles high. The ejections from our sun 



246 



ASTRONOMY 



under those circumstances are most violent and to the greatest 
distances in the directions toward and away from S x . For simplicity, 
let us consider only the matter ejected toward S x . If S 1 were 
standing still this matter would proceed toward it a certain distance, 
depending upon the speed with which it left the sun, and then would 
either fall back upon the sun or go to S lt depending upon which 
had the dominating attraction for it. But instead of standing still 
£j is moving forward rapidly in its orbit. Suppose the direction of 
motion is that indicated by the arrow in Fig. 108. After a certain 
interval Si has moved forward to the point S 2 . At this place it is 
attracting the ejected mass P nearly at right angles to its original 
line of projection. Consequently, it causes its orbit to curve in the 
direction in which Si is going. The visiting star will go on in its 




Fig. 109. The Origin of a Spiral Nebula 



orbit and leave P behind revolving around the sun in the dotted 
ellipse C. In a similar manner the mass P will be bent from the 
straight line of its ejection in the direction indicated in the diagram, 
and will be left revolving in the ellipse C ' . Therefore, as the visiting 
star passes near the sun it stimulates the ejection of material and 
causes it to deviate from the original line of its motion so that instead 
of falling back on the sun it is left revolving about it in elliptical 
orbits. 

This process of ejection obviously would not take place at only 
one instant, while Si was passing our sun. We now consider the 
result of its taking place continually during the passage. Many 
particles are ejected and they move along the dotted lines of Fig. 
109. At a given time they are on the full lines of Fig. 109, which 
are seen to constitute the arms of a spiral with two approximately 
symmetrical parts. If this theory is correct, we should find that the 
spiral nebulas have two arms reaching out from a central sun in 



ASTRONOMY 247 

opposite directions which are curved in the same direction. The 
particles on the spiral are not moving along its arms, but approxi- 
mately at right angles to them. The particles near the center move 
faster than those far away, and consequently the older the spiral 
nebula and the larger its central mass relatively to the total mass 
of the scattered material, the closer is its coil. 




Fig. 110. Spiral Nebula in Canes Venatici. Photographed at the 
Yerkes Observatory 

The question now arising is whether the spiral nebulas which 
are known have the characteristics which would be predicted 
according to this theory. Fig. 110 is a photograph of one of these 
objects. It is seen that it is composed of two arms, in a general 
way symmetrical, which reach out from the opposite sides of a central 
nucleus, or sun. It is found that thev always have two arms which 



248 ASTRONOMY 

can be more or less definitely made out, radiating from the center 
in this fashion. The suggestion of their origin seems to be in 
harmony with their appearance, though it can not be regarded as 
demonstrated that this is the true explanation of their mode of 
development. Fig. Ill shows one of these objects which is edgewise 




Fig. 111. Spiral Nebula in Adromed Seen Edgewise. The Dark Peripheral Material | 
Causes a Dark Streak by Eclipse. Photographed at the Lick Observatory 

to us. The dark streak down it is due to opaque, cooler absorbing 
material on its periphery. 

According to the planetesimal theory the planets grew up around 
the nuclei on the arms of the spirals from which our system devel- 
oped, whatever may have been its origin. It is clear that if the 
origin of the spiral were as outlined above, we should not expect to 
find the arms perfectly uniform because the ejection from our sun 
would not take place uniformly. The photographs show many 



ASTRONOMY 249 

irregularities and local condensations on the arms. These nuclei 
circulating around the central sun and crossing the orbits of many 
other particles also circulating around the center, gradually sweep 
them up and in the course of time absorb all or Che small masses 
in the system whose orbits they cross. In this manner there eventu- 
ally evolves a system consisting of a central sun and a number of 
large masses spaced out so that they never approach very near one 
another, and no small ones except possibly in zones which were not 
occupied by any dominant nucleus. 

Let us see whether this theory is in harmony with the chief 
facts presented by the solar system. According to it all the planets 
should revolve in the same direction, and such is found to be the 
case. According to it their planes should be approximately the 
same, though not necessarily the same, for the initial ejections would 
not necessarily be exactly toward or from the passing sun. Here, 
again, the theory and observations are in harmony. According to 
this theory the planets are all the same age, and the differences in 
the state of their development are only because of their different 
dimensions and different constitutions. The facts given by obser- 
vation are in this respect much more in harmony with this theory 
than with the Laplacian. One of the difficulties, at least at first 
thought, arises from the fact that when the visiting sun had passed 
on, the orbits of the individual nuclei and particles should be on 
the average considerably more eccentric than the orbits of the 
planets. But a mathematical examination of the question shows that 
the orbits of the planets become more nearly circular on account of 
their collisions with the scattered material which the planets sweep 
up in their motions around the sun. Consequently, the more a 
planet grows by the accretion of this scattered material the more 
nearly circular its orbit becomes. It is significant that in our 
system the great planets all have very nearly circular orbits, while 
the smaller ones have more elongated orbits, and the orbits of the 
planetoids are in many cases very much elongated. There is here 
perfect harmony between the theory and the facts given by observa- 
tions. Similar results follow when we consider the inclinations of the 
orbits to one another. The more matter a planetary nucleus acquires 
by collision with the scattered material, the more nearly will its 
orbit fall into the average plane of the system. It is found that 



250 ASTRONOMY 

the great planets move in orbits which are almost in the same plane, 
while the smaller ones deviate some, and in many cases the planetoids 
very much. Thus, again, there is harmony between theory and 
observations. 

In discussing the Laplacian theory, it was found that difficulties 
arise because of the retrograde revolution of certain satellites. 
The question arises whether the planetesimal theory has difficulties 
in this same respect. According to the planetesimal theory the 
satellites have evolved from small secondary nuclei which were revolv- 
ing around the central sun in close proximity to the larger nuclei 
which developed into planets. There is no reason why these sec- 
ondary nuclei should not originally have revolved around the planets 
in any direction. A discussion of the matter shows that those which 
revolve in any direction except in that in which the planet revolves 
have a tendency, because of collisions w r ith the scattered material, 
to fall upon the planet and to become a part of it. This is particu- 
larly true unless they are far from it. Consequently, we should 
expect to find the satellites on the whole revolving in the forward 
direction, though not necessarily all in that direction. And further- 
more, there is no reason according to this theory why a satellite 
should not revolve around the planet in a shorter period than that 
of the rotation of the planet itself. 

According to the Laplacian theory it is difficult to account 
for the forward rotations of the planets. The forward rotation of 
the planets is to be expected under the planetesimal theory, because 
it can be shown that the collisions of the scattered material with 
the planetary nuclei have, on the average, a tendency to make them 
rotate in the direction of their revolution. This tendency is, besides, 
the greatest in their equatorial zones, and if they are in a fluid state 
should give to their equators a greater speed of rotation than to the 
higher latitudes. All of these consequences of the theory are in per- 
fect harmony with the facts. 

Conclusion. We shall sum up in a few words the general picture 
of the origin and development of astronomical bodies, remembering, 
however, that the problem is a vast one and that the chances for 
actual errors and imperfections in our theories are very great. We 
regard matter as being in its most primitive state when it is spread 
out in widely-scattered, irregular nebulas. (See Fig. 104.) These 



ASTRONOMY 251 

objects are supposed to develop continually; that is, they are sup- 
posed not only to have originated in the past, but are even now 
being evolved, and will continue to evolve in the future. These 
nebulous masses, under the chemical and gravitational forces, became 
organized into suns and systems of suns. The suns now and then 
passing near one another develop spiral nebulas. The nuclei on the 
arms of the spirals, sweeping up this finely scattered material, grow 
into planets, or at any rate into bodies secondary in dimensions com- 
pared with the central sun. The length of time required for this 
evolution is altogether beyond calculation at the present time. 
Considering the earth, we think of it as having grown up rapidly 
at first, and more slowly later, by the accretion of the scattered 
material. Originally it was perhaps too small to hold an atmosphere, 
which was subsequently acquired by the expulsion of gases from the 
material of which it was composed, as it ground together under 
pressure and became heated by its contraction. After acquiring 
an atmosphere and water it became habitable, at least for low forms 
of life. At the present time it is not growing at a sensible rate, and 
so far as can be seen will remain approximately in its present state 
for an extremely long time. It seems to be threatened only by a 
possible failure of the sun's light and heat. Until we know more 
exactly than at the present time the sources of the sun's heat, we 
can not estimate how soon the changes in the amount of light and 
heat received from the sun will have sensible influences upon the 
earth. One event in the remote future seems probable, if not certain. 
It is that once again our sun will pass near some other sun, when 
the present planetary system will be destroyed, perhaps to give 
place to a new one running through a somewhat similar cycle. 



INDEX 



A Page 

Astronomical problems respecting earth 7 

Astronomy 1-251 

comets and meteors , 185 

constellations 61 

cosmogony, or the evolution of worlds . 235 

earth as an astronomical body 7 

moon , 110 

preliminary considerations 1 

sidereal system 216 

solar system 137 

sun ; 197 

time 100 

Atmosphere 

effects of, on climate 25 

escape of 23 

of moon 120 

refraction of light by 28 



B 
Bootes 95 



C 

Calendar 109 

Canis Major 100 

Cassiopeia 92 

Civil and astronomical days 107 

Comets 

capture of 187 

celebrated 190 

dimensions and masses of 186 

orbits of 185 

Comets and meteors, relation of 194 

Constellations 61 

application of declination to location of stars 71 

Bootes 95 

Canis Major 1 00 

Cassiopeia 92 

determination of right ascension of meridian at any time 69 

Gemini 1 00 



254 INDEX 

Page 
Constellations 

Leo 96 

magnitudes of stars 82 

Milky Way 88 

naming the stars • 79 

number of stars 85 

origin of 72 

Orion 97 

pole star 90 

problem of locating 61 

proper motions of stars 87 

Scorpio 95 

star catalogues 80 

systems of coordinates for locating 

comparison of 68 

ecliptic 67 

equator 64 

geographical 62 

horizon 63 

Taurus 96 

Cosmogony 235 

evolution 235 

historical 237 

planetesimal theory 244 

test of Laplacian theory 241 

D 
Distance 

of moon 113 

of planets 141 

of sun 141 

of stars 218 

E 

Earth as an astronomical body 7 

astronomical problems respecting 7 

condition of interior of 15 

density of 14 

oblateness of 10 

orbit of 48 

proofs of its sphericity 8 

revolution of 44 

rotation of 30 

size of 13 

Earth's atmosphere 

climatic effects of t 25 

composition of 18 

height of 18 

Earth's orbit, shape of 48 



INDEX 255 

Page 
Eclipses 

of moon 131 

of sun 132 

Ecliptic, obliquity of 49 

Ecliptic systems of coordinates 67 

Equator system of coordinates 64 

Equinoxes, precession of 50 

Evolution 235 

F 

First-magnitude stars 85 

G 

Gases, kinetic theory of 21 

Gemini 100 

Geographical system of coordinates 62 

H 

Horizon system of coordinates 63 

J 

Jupiter 170 

L 

Laplacian theory, test of 241 

Latitude 

different kinds of 13 

variation of 40 

Laws 

of gravitation 139 

of motion 32 

Leo 96 

Light and heat received from sun 197 

Lyra 93 

M 

Magnitudes of stars 82 

Mars 161 

Mass of moon 119 

Mean solar time 103 

Mercury and Venus 159 

Meteorites 196 

Meteors or shooting stars 192 

influences of, on the earth 195 

meteorites 196 

relation of comets and meteors 194 



256 INDEX 

i Page 

Milky Way or galaxy 88 

Moon 110 

actual motion of 117 

apparent motion among stars 110 

atmosphere of 120 

distance of 113 

distribution of sunlight and moonlight 113 

eclipses of 131 

eclipses of sun , 132 

light and heat received by earth from 121 

mass of 119 

phases of Ill 

relative number of eclipses of sun and moon as observed from any 

one place 133 

size of 118 

surface conditions on 123 

temperature of 122 

Motion, laws of 32 

N 

Neptune • 181 

O 

Orbits of planets 138 

Origin of constellations 72 

Orion ,. . .' 97 



P 

Place of change of date 107 

Planetesimal theory 244 

Planetoids 152 

Planets 

dimensions and masses of 144 

distances of 141 

periods of 147 

two groups of 151 

Pole star, how to find 90 

R 

Revolution of earth 
proved by 

aberration of light. 46 

laws of motion 42 

parallax of stars 44 

spectroscope 47 

Right ascension of meridian 69 



INDEX 257 

Page 

Rotation of earth 30 

analogy with other heavenly bodies 37 

laws of motion 32 

proved by eastward deviation of falling bodies 34 

proved by Foucault's pendulum experiment 36 

proved by its shape 35 

uniformity of 38 

S 

Saturn . . .' 175 

Science 

contributions of astronomy to 3 

origin of 2 

value of 1 

Scorpio 95 

Seasons 

causes of 51 

effect of eccentricity of earth's orbit upon 58 

lag of 57 

Sidereal system 216 

distribution of stars ' 216 

double stars 224 

groups of stars 219 

nebulas 233 

spectroscopic binary stars 227 

temporary stars 231 

variable stars 229 

Sidereal month Ill 

Sidereal time 101 

Sidereal year 108 

Size of moon 118 

Solar system 137 

dimensions and masses of planets 144 

distances of planets 141 

historical 237 

Jupiter 170 

law of gravitation 139 

Mars 161 

members of 137 

Mercury and Venus 159 

Neptune 1S1 

orbits of planets 138 

periods of planets 147 

planetoids 152 

Saturn 175 

two groups of planets 151 

Uranus 179 

zodiacal light and gegenschein 157 

Solar time 102 



258 INDEX 

Page 

Spectrum analysis 210 

Star catalogues 80 

Stars 

distribution of 216 

double 224 

first-magnitude 85 

groups of . .' 219 

location of 71 

magnitudes of 82 

Milky Way 88 

naming of 79 

nebulas 233 

number of . 85 

Pole star 90 

proper motions of 87 

spectroscopic binary 227 

temporary 231 

variable 229 

Sun 197 

different layers of 206 

light and heat received from 197 

motion of, with respect to stars 42 

source of heat of 200 

spectrum analysis 210 

spots 204 

Sunlight and moonlight, distribution of 113 

Surface conditions on moon 123 



T 
Table 

binary stars whose masses and distances are known 226 

comparative gravity of sun and planets 147 

data from which to compute times favorable for observation of planets 150 

densities of sun and planets 146 

list of constellations with right ascensions and declinations 73 

list of first-magnitude stars 84 

number of stars visible to naked eye 85 

planets in order from sun with apparent and actual diameters 144 

surface and volume of planets as compared to earth 145 

Taurus 96 

Temperature of moon 122 

Time 100 

calendar 109 

civil and astronomical days 107 

definition of equal intervals of 100 

mean solar 103 

place of change of date , 107 

sidereal 101 

sidereal year 108 



INDEX 259 

Page 

Time 

solar * 102 

standard 105 

Tropical year 108 

U 

Uranus ......,, 179 

Z 

Zodiacal light and gegenschein 157 



